Pub Date : 2024-04-23DOI: 10.1080/03605302.2024.2341055
Robert Schippa
We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are ...
{"title":"Strichartz estimates for Maxwell equations in media: the partially anisotropic case","authors":"Robert Schippa","doi":"10.1080/03605302.2024.2341055","DOIUrl":"https://doi.org/10.1080/03605302.2024.2341055","url":null,"abstract":"We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are ...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"28 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-27DOI: 10.1080/03605302.2024.2302017
Ambre Chabert
We build a smooth real potential V(t, x) on (t0,+∞)×R2 decaying to zero as t→∞ and a smooth solution to the associated perturbed cubic noninear harmonic oscillator whose Sobolev norms blow up log...
{"title":"A weakly turbulent solution to the cubic nonlinear harmonic oscillator on ℝ2 perturbed by a real smooth potential decaying to zero at infinity","authors":"Ambre Chabert","doi":"10.1080/03605302.2024.2302017","DOIUrl":"https://doi.org/10.1080/03605302.2024.2302017","url":null,"abstract":"We build a smooth real potential V(t, x) on (t0,+∞)×R2 decaying to zero as t→∞ and a smooth solution to the associated perturbed cubic noninear harmonic oscillator whose Sobolev norms blow up log...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"67 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139589782","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-17DOI: 10.1080/03605302.2024.2302377
Fabian Rupp
We introduce a non-local L2-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, w...
{"title":"The Willmore flow with prescribed isoperimetric ratio","authors":"Fabian Rupp","doi":"10.1080/03605302.2024.2302377","DOIUrl":"https://doi.org/10.1080/03605302.2024.2302377","url":null,"abstract":"We introduce a non-local L2-gradient flow for the Willmore energy of immersed surfaces which preserves the isoperimetric ratio. For spherical initial data with energy below an explicit threshold, w...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"482 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-17DOI: 10.1080/03605302.2023.2300824
Annalisa Cesaroni, Marco Cirant
Recently, R. Carmona, Q. Cormier, and M. Soner proposed a Mean Field Game (MFG) version of the classical Kuramoto model, which describes synchronization phenomena in a large population of “rational...
{"title":"Stationary equilibria and their stability in a Kuramoto MFG with strong interaction","authors":"Annalisa Cesaroni, Marco Cirant","doi":"10.1080/03605302.2023.2300824","DOIUrl":"https://doi.org/10.1080/03605302.2023.2300824","url":null,"abstract":"Recently, R. Carmona, Q. Cormier, and M. Soner proposed a Mean Field Game (MFG) version of the classical Kuramoto model, which describes synchronization phenomena in a large population of “rational...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"17 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139518746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-01-07DOI: 10.1080/03605302.2023.2295035
Georgios Mavrogiannis
We give an elementary new argument for global existence and exponential decay of solutions of quasilinear wave equations on Schwarzschild–de Sitter black hole backgrounds, for appropriately small i...
我们给出了一个新的基本论证，即在施瓦兹希尔德-德-西特黑洞背景上，对于适当的小i...
{"title":"Quasilinear wave equations on Schwarzschild–de Sitter","authors":"Georgios Mavrogiannis","doi":"10.1080/03605302.2023.2295035","DOIUrl":"https://doi.org/10.1080/03605302.2023.2295035","url":null,"abstract":"We give an elementary new argument for global existence and exponential decay of solutions of quasilinear wave equations on Schwarzschild–de Sitter black hole backgrounds, for appropriately small i...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"54 9 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139460977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-29DOI: 10.1080/03605302.2023.2296924
Rémi Carles, Guillaume Ferriere
We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, whi...
{"title":"Logarithmic Gross-Pitaevskii equation","authors":"Rémi Carles, Guillaume Ferriere","doi":"10.1080/03605302.2023.2296924","DOIUrl":"https://doi.org/10.1080/03605302.2023.2296924","url":null,"abstract":"We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, whi...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"18 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139065753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-23DOI: 10.1080/03605302.2023.2292992
Jeremy G. Hoskins, Hadrian Quan, Stefan Steinerberger
We study localization properties of low-lying eigenfunctions of magnetic Schrödinger operators (−i∇−A(x))2ϕ+V(x)ϕ=λϕ, where V:Ω→R≥0 is a given potential and A:Ω→Rd induces a magnetic field. We e...
{"title":"Magnetic Schrödinger operators and landscape functions","authors":"Jeremy G. Hoskins, Hadrian Quan, Stefan Steinerberger","doi":"10.1080/03605302.2023.2292992","DOIUrl":"https://doi.org/10.1080/03605302.2023.2292992","url":null,"abstract":"We study localization properties of low-lying eigenfunctions of magnetic Schrödinger operators (−i∇−A(x))2ϕ+V(x)ϕ=λϕ, where V:Ω→R≥0 is a given potential and A:Ω→Rd induces a magnetic field. We e...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"78 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139027838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-20DOI: 10.1080/03605302.2023.2294335
Antonio De Rosa, Reinaldo Resende
We prove that m-dimensional Lipschitz graphs in any codimension with C1,α boundary and anisotropic mean curvature bounded in Lp, p > m, are regular at every boundary point with density bounded abov...
{"title":"Boundary regularity for anisotropic minimal Lipschitz graphs","authors":"Antonio De Rosa, Reinaldo Resende","doi":"10.1080/03605302.2023.2294335","DOIUrl":"https://doi.org/10.1080/03605302.2023.2294335","url":null,"abstract":"We prove that m-dimensional Lipschitz graphs in any codimension with C1,α boundary and anisotropic mean curvature bounded in Lp, p > m, are regular at every boundary point with density bounded abov...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"32 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138818330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-30DOI: 10.1080/03605302.2023.2283830
Leon Bungert
The purpose of this paper is to prove a uniform convergence rate of the solutions of the p-Laplace equation Δpu=0 with Dirichlet boundary conditions to the solution of the infinity-Laplace equation...
{"title":"The convergence rate of p-harmonic to infinity-harmonic functions","authors":"Leon Bungert","doi":"10.1080/03605302.2023.2283830","DOIUrl":"https://doi.org/10.1080/03605302.2023.2283830","url":null,"abstract":"The purpose of this paper is to prove a uniform convergence rate of the solutions of the p-Laplace equation Δpu=0 with Dirichlet boundary conditions to the solution of the infinity-Laplace equation...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"36 15","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-14DOI: 10.1080/03605302.2023.2277453
Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie
In this follow up but self contained paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of i...
{"title":"Nonlinear enhanced dissipation in viscous Burgers type equations II","authors":"Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie","doi":"10.1080/03605302.2023.2277453","DOIUrl":"https://doi.org/10.1080/03605302.2023.2277453","url":null,"abstract":"In this follow up but self contained paper, we focus on the viscous Burgers equation. There, using the Hopf-Cole transformation, we compute the long time behavior of solutions for some classes of i...","PeriodicalId":50657,"journal":{"name":"Communications in Partial Differential Equations","volume":"35 5","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138506095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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