Pub Date : 2023-08-20DOI: 10.1080/17476933.2023.2247998
Kaushik Mohanta, J. Tyagi
We study the following version of Hardy-type inequality on a domain $Omega$ in a Riemannian manifold $(M,g)$: $$ int{Omega}|nabla u|_g^prho^alpha dV_g geq left(frac{|p-1+beta|}{p}right)^pint{Omega}frac{|u|^p|nabla rho|_g^p}{|rho|^p}rho^alpha dV_g +int{Omega} V|u|^prho^alpha dV_g, quad forall uin C_c^infty (Omega). $$ We provide sufficient conditions on $p, alpha, beta,rho$ and $V$ for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities on Riemannian manifolds. The functional setup covers a wide variety of particular cases, which are discussed briefly: for example, $mathbb{R}^N$ with $p
{"title":"Improved hardy inequalities on Riemannian manifolds","authors":"Kaushik Mohanta, J. Tyagi","doi":"10.1080/17476933.2023.2247998","DOIUrl":"https://doi.org/10.1080/17476933.2023.2247998","url":null,"abstract":"We study the following version of Hardy-type inequality on a domain $Omega$ in a Riemannian manifold $(M,g)$: $$ int{Omega}|nabla u|_g^prho^alpha dV_g geq left(frac{|p-1+beta|}{p}right)^pint{Omega}frac{|u|^p|nabla rho|_g^p}{|rho|^p}rho^alpha dV_g +int{Omega} V|u|^prho^alpha dV_g, quad forall uin C_c^infty (Omega). $$ We provide sufficient conditions on $p, alpha, beta,rho$ and $V$ for which the above inequality holds. This generalizes earlier well-known works on Hardy inequalities on Riemannian manifolds. The functional setup covers a wide variety of particular cases, which are discussed briefly: for example, $mathbb{R}^N$ with $p","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44419678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-10DOI: 10.1080/17476933.2023.2244884
Adam B. Christopherson, Kenneth D. Koenig
{"title":"Weak-type regularity of the Bergman projection on generalized Hartogs triangles in C3","authors":"Adam B. Christopherson, Kenneth D. Koenig","doi":"10.1080/17476933.2023.2244884","DOIUrl":"https://doi.org/10.1080/17476933.2023.2244884","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41621200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-26DOI: 10.1080/17476933.2023.2236942
Abderrahmane Lakhdari, K. Tahri, N. B. Rhouma
{"title":"The uniqueness solution for a fractional φ-Laplacian Dirichlet problem and its spectrum","authors":"Abderrahmane Lakhdari, K. Tahri, N. B. Rhouma","doi":"10.1080/17476933.2023.2236942","DOIUrl":"https://doi.org/10.1080/17476933.2023.2236942","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46122158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-24DOI: 10.1080/17476933.2023.2236970
Y. Sang, Z. Han, Xue Yu
{"title":"Fractional nonhomogeneous system with Hardy-Littlewood-Sobolev critical nonlinearity","authors":"Y. Sang, Z. Han, Xue Yu","doi":"10.1080/17476933.2023.2236970","DOIUrl":"https://doi.org/10.1080/17476933.2023.2236970","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":"2015 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41305312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-24DOI: 10.1080/17476933.2023.2236943
Natham Aguirre
{"title":"p-harmonic functions with nonlinear Neumann conditions on the sphere and measure data","authors":"Natham Aguirre","doi":"10.1080/17476933.2023.2236943","DOIUrl":"https://doi.org/10.1080/17476933.2023.2236943","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44745520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-20DOI: 10.1080/17476933.2023.2234830
H. T. Phương, Inthavichit Padaphet
{"title":"A uniqueness theorem for holomorphic curves on annulus sharing hypersurfaces","authors":"H. T. Phương, Inthavichit Padaphet","doi":"10.1080/17476933.2023.2234830","DOIUrl":"https://doi.org/10.1080/17476933.2023.2234830","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47150921","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-09DOI: 10.1080/17476933.2023.2229745
M. Efendiev, V. Vougalter
: The article is devoted to the existence of solutions of a system of integro-differential equations involving the drift terms in the case of the normal diffusion and the influx/efflux terms proportional to the Dirac delta function. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non- Fredholm elliptic operators in unbounded domains. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities. , ,
{"title":"On the solvability of some systems of integro-differential equations with transport and concentrated sources","authors":"M. Efendiev, V. Vougalter","doi":"10.1080/17476933.2023.2229745","DOIUrl":"https://doi.org/10.1080/17476933.2023.2229745","url":null,"abstract":": The article is devoted to the existence of solutions of a system of integro-differential equations involving the drift terms in the case of the normal diffusion and the influx/efflux terms proportional to the Dirac delta function. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non- Fredholm elliptic operators in unbounded domains. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities. , ,","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48425345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-02DOI: 10.1080/17476933.2023.2229736
A. H. Benhana
{"title":"Multiplicity of solutions for the stationary quantum Zakharov system with combined nonlinearities","authors":"A. H. Benhana","doi":"10.1080/17476933.2023.2229736","DOIUrl":"https://doi.org/10.1080/17476933.2023.2229736","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46792741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-02DOI: 10.1080/17476933.2023.2229746
Nguyen Van Trao, Nguyen Xuan Hong, Pham Nguyen Thu Trang
{"title":"Hölder continuity of solutions of the Dirichlet problem in pseudoconvex domains","authors":"Nguyen Van Trao, Nguyen Xuan Hong, Pham Nguyen Thu Trang","doi":"10.1080/17476933.2023.2229746","DOIUrl":"https://doi.org/10.1080/17476933.2023.2229746","url":null,"abstract":"","PeriodicalId":51229,"journal":{"name":"Complex Variables and Elliptic Equations","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46218324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：