Zobrazeno 1 - 6
of 6
pro vyhledávání: '"Tomás Sanz-Perela"'
Publikováno v:
Mathematics in Engineering, Vol 3, Iss 5, Pp 1-36 (2021)
This paper addresses saddle-shaped solutions to the semilinear equation $L_K u = f(u)$ in $\mathbb{R}^{2m}$, where $L_K$ is a linear elliptic integro-differential operator with a radially symmetric kernel $K$, and $f$ is of Allen-Cahn type. Saddle-sh
Externí odkaz:
https://doaj.org/article/3763399190ce43c7a9622b8bb3bf9913
Publikováno v:
Communications in Mathematical Physics. 397:337-392
We study spectral properties of Dirac operators on bounded domains $\Omega \subset \mathbb{R}^3$ with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter $\tau\in\mathbb{R}$; the case $\tau = 0$ corresponds to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c8db48e18deefd11d32580e8f6d64fea
https://doi.org/10.1007/s00220-022-04526-3
https://doi.org/10.1007/s00220-022-04526-3
Publikováno v:
Revista Matemática Iberoamericana. 36:1887-1916
In this paper we prove the uniqueness of the saddle-shaped solution to the semilinear nonlocal elliptic equation $(-\Delta)^\gamma u = f(u)$ in $\mathbb R^{2m}$, where $\gamma \in (0,1)$ and $f$ is of Allen-Cahn type. Moreover, we prove that this sol
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9600f900c9c3004776a9c56fb0769a49
https://doi.org/10.4171/rmi/1185
https://doi.org/10.4171/rmi/1185
Autor:
Xavier Cabré, Tomás Sanz-Perela
We study stable solutions to the equation $(-\Delta)^{1/2} u = f(u)$, posed in a bounded domain of $\mathbb{R}^n$. For nonnegative convex nonlinearities, we prove that stable solutions are smooth in dimensions $n\leq 4$. This result, which was known
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::13dbe780d084ab4463fcfbae9df4ceb6
http://arxiv.org/abs/2110.02245
http://arxiv.org/abs/2110.02245
This is the first of two papers concerning saddle-shaped solutions to the semilinear equation L K u = f ( u ) in R 2 m , where L K is a linear elliptic integro-differential operator and f is of Allen-Cahn type. Saddle-shaped solutions are doubly radi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a4f7eb84c9711059f71c8f270f431eac
Autor:
Tomás Sanz-Perela
Publikováno v:
Recercat. Dipósit de la Recerca de Catalunya
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
instname
UPCommons. Portal del coneixement obert de la UPC
Universitat Politècnica de Catalunya (UPC)
We study the regularity of stable solutions to the problem \begin{document}$\begin{align}\left\{ \begin{gathered} {\left( { - \Delta } \right)^s}u\;{B_1}, \hfill \\ u\;{{\mathbb{R}}^n}\backslash {B_1}, \hfill \\ \end{gathered} \right.\end{align}$ \en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::93700a6bd6d53b538f749d0e3d57d036
http://arxiv.org/abs/1712.08598
http://arxiv.org/abs/1712.08598