Bilinear forms on non-homogeneous Sobolev spaces
In this paper we show that if $b\in L^2(\R^n)$, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces $H_s^2(\R^n)\times H_s^2(\R^n)$, $0<s<1$ by $$ (f,g)\in H_s^2(\R^n)\times H_s^2(\R^n) \to \int_{\R^n} (Id-\Delta)^{s/2}(fg)({\bf x}) b({\bf x})d{\bf x}, $$ is con...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/193292 |
| Acesso em linha: | https://hdl.handle.net/2445/193292 |
| Access Level: | acceso abierto |
| Palavra-chave: | Anàlisi funcional Espais de Sobolev Equacions en derivades parcials Equacions diferencials el·líptiques Functional analysis Sobolev spaces Partial differential equations Elliptic differential equations |
| Resumo: | In this paper we show that if $b\in L^2(\R^n)$, then the bilinear form defined on the product of the non-homogeneous Sobolev spaces $H_s^2(\R^n)\times H_s^2(\R^n)$, $0<s<1$ by $$ (f,g)\in H_s^2(\R^n)\times H_s^2(\R^n) \to \int_{\R^n} (Id-\Delta)^{s/2}(fg)({\bf x}) b({\bf x})d{\bf x}, $$ is continuous if and only if the positive measure $|b({\bf x})|^2d{\bf x} $ is a trace measure for $H_s^2(\R^n)$. |
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