Pub Date : 2005-06-10DOI: 10.1080/02781070500130665
R. Saks, C. J. Vanegas
The boundary value problem for the linear weakly elliptic system in the ball G of is studied and three methods for finding the solution of it in the space are derived. In order to reach this goal, it is used with the theory of potentials, spectral theory and a complex form of this system is considered.
{"title":"Solution of one boundary value problem for curl, +λ I operator in the ball","authors":"R. Saks, C. J. Vanegas","doi":"10.1080/02781070500130665","DOIUrl":"https://doi.org/10.1080/02781070500130665","url":null,"abstract":"The boundary value problem for the linear weakly elliptic system in the ball G of is studied and three methods for finding the solution of it in the space are derived. In order to reach this goal, it is used with the theory of potentials, spectral theory and a complex form of this system is considered.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"64 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128261652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500156835
Song-Hua Li, Wei Lin
In this article, we first apply the contour integral method to generalize the Shannon–Whittaker theorem to the case for the multi-valued analytic functions. Based on this result we obtain the numerical solution for the Helmholtz equation. In order to overcome the difficulty that the coerciveness does not hold, we prove the existence and uniqueness of the solution to Helmholtz equation with the third boundary condition in the upper half plane.
{"title":"A numerical method based on the generalized Shannon–Whittaker representation theorem for solving Helmholtz equation","authors":"Song-Hua Li, Wei Lin","doi":"10.1080/02781070500156835","DOIUrl":"https://doi.org/10.1080/02781070500156835","url":null,"abstract":"In this article, we first apply the contour integral method to generalize the Shannon–Whittaker theorem to the case for the multi-valued analytic functions. Based on this result we obtain the numerical solution for the Helmholtz equation. In order to overcome the difficulty that the coerciveness does not hold, we prove the existence and uniqueness of the solution to Helmholtz equation with the third boundary condition in the upper half plane.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122510921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086958
Ajay Kumar, R. Prakash
Explicit representations of the solution to higher-order Poisson equation with Dirichlet boundary conditions are obtained. The equations for 1 ≤ m, n have also been investigated.
得到了具有Dirichlet边界条件的高阶泊松方程解的显式表示。本文还研究了1≤m, n时的方程。
{"title":"Boundary value problems for the Poisson equation and bi-analytic functions","authors":"Ajay Kumar, R. Prakash","doi":"10.1080/02781070500086958","DOIUrl":"https://doi.org/10.1080/02781070500086958","url":null,"abstract":"Explicit representations of the solution to higher-order Poisson equation with Dirichlet boundary conditions are obtained. The equations for 1 ≤ m, n have also been investigated.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122304654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070512331389550
{"title":"HB in a favourite T (artist unknown)","authors":"","doi":"10.1080/02781070512331389550","DOIUrl":"https://doi.org/10.1080/02781070512331389550","url":null,"abstract":"","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127115258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500087600
L. Son, W. Tutschke
From the very beginning, Complex Analysis is closely connected with partial differential equations. The article surveys present generalizations of these connexions to higher dimensions.
复分析从一开始就与偏微分方程密切相关。本文调查了这些联系在高维上的推广。
{"title":"Complex methods in higher dimensions – recent trends for solving boundary value and initial value problems","authors":"L. Son, W. Tutschke","doi":"10.1080/02781070500087600","DOIUrl":"https://doi.org/10.1080/02781070500087600","url":null,"abstract":"From the very beginning, Complex Analysis is closely connected with partial differential equations. The article surveys present generalizations of these connexions to higher dimensions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122415906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086842
G. Hile, A. Stanoyevitch
We investigate Cauchy problems for complex differential equations of the form , where is a Bessel differential operator in the “time variable”, and a linear differential operator in the “space variables”, possibly also involving Bessel operators. We establish conditions for existence and uniqueness of polynomial solutions whenever the Cauchy data is polynomial, and we give explicit formulas for these solutions. When the Cauchy data consists of monomials, these polynomial solutions are analogous to the heat polynomials for the heat equation.
{"title":"Polynomial solutions to Cauchy problems for complex Bessel operators","authors":"G. Hile, A. Stanoyevitch","doi":"10.1080/02781070500086842","DOIUrl":"https://doi.org/10.1080/02781070500086842","url":null,"abstract":"We investigate Cauchy problems for complex differential equations of the form , where is a Bessel differential operator in the “time variable”, and a linear differential operator in the “space variables”, possibly also involving Bessel operators. We establish conditions for existence and uniqueness of polynomial solutions whenever the Cauchy data is polynomial, and we give explicit formulas for these solutions. When the Cauchy data consists of monomials, these polynomial solutions are analogous to the heat polynomials for the heat equation.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123029660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500083013
A. Soldatov
The boundary value problems for elliptic systems of the second order with leading and constant coefficients are considered in a half-plane. The investigation is based on the Bitsadze formula which represents a general solution of this system through a vector-valued analytic function. The transformation of this formula is studied in Holder spaces with weight. As a consequence, the explicit formulas of the solution to the problems are received. The applications to anisotropic elasticity are also given.
{"title":"On elliptic boundary value problems on upper half-plane","authors":"A. Soldatov","doi":"10.1080/02781070500083013","DOIUrl":"https://doi.org/10.1080/02781070500083013","url":null,"abstract":"The boundary value problems for elliptic systems of the second order with leading and constant coefficients are considered in a half-plane. The investigation is based on the Bitsadze formula which represents a general solution of this system through a vector-valued analytic function. The transformation of this formula is studied in Holder spaces with weight. As a consequence, the explicit formulas of the solution to the problems are received. The applications to anisotropic elasticity are also given.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126205119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500130715
O. Calin, D. Chang
We discuss the sub-Riemannian geometry induced by the sub-Laplacian Δk on a family of finite type, pseudoconvex hypersurfaces . We also give the physical interpretation of this geometry.
{"title":"Geometric analysis on a family of pseudoconvex hypersurfaces","authors":"O. Calin, D. Chang","doi":"10.1080/02781070500130715","DOIUrl":"https://doi.org/10.1080/02781070500130715","url":null,"abstract":"We discuss the sub-Riemannian geometry induced by the sub-Laplacian Δk on a family of finite type, pseudoconvex hypersurfaces . We also give the physical interpretation of this geometry.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122725257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500086677
Jinyuan Du, Yufeng Wang
In this article, Riemann boundary value problems (BVPs) of polyanalytic functions and metaanalytic functions on the closed curve are investigated. Using the theorem of decomposition of polyanalytic functions, the expression of solution and the condition of solvability for Riemann BVP of polyanalytic functions are obtained by reducing the problem to the equivalent Riemann BVP of analytic functions. Then the expression of solution and the condition of solvability for Riemann BVP of metaanalytic functions are obtained by reducing the problem into the equivalent Riemann BVP of polyanalytic functions.
{"title":"Riemann boundary value problems of polyanalytic functions and metaanalytic functions on the closed curves","authors":"Jinyuan Du, Yufeng Wang","doi":"10.1080/02781070500086677","DOIUrl":"https://doi.org/10.1080/02781070500086677","url":null,"abstract":"In this article, Riemann boundary value problems (BVPs) of polyanalytic functions and metaanalytic functions on the closed curve are investigated. Using the theorem of decomposition of polyanalytic functions, the expression of solution and the condition of solvability for Riemann BVP of polyanalytic functions are obtained by reducing the problem to the equivalent Riemann BVP of analytic functions. Then the expression of solution and the condition of solvability for Riemann BVP of metaanalytic functions are obtained by reducing the problem into the equivalent Riemann BVP of polyanalytic functions.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"136 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132656504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2005-06-10DOI: 10.1080/02781070500138817
R. Gilbert, Yongzhi S. Xu
In this article we construct the three-dimensional Green's function for Helmholtz's equation in a layered half-space.
本文构造了分层半空间中亥姆霍兹方程的三维格林函数。
{"title":"Green's function for the Helmholtz equation in a layered half-space","authors":"R. Gilbert, Yongzhi S. Xu","doi":"10.1080/02781070500138817","DOIUrl":"https://doi.org/10.1080/02781070500138817","url":null,"abstract":"In this article we construct the three-dimensional Green's function for Helmholtz's equation in a layered half-space.","PeriodicalId":272508,"journal":{"name":"Complex Variables, Theory and Application: An International Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2005-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127838493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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