Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/193292
Title: | Bilinear forms on non-homogeneous Sobolev spaces |
Author: | Cascante, Ma. Carme (Maria Carme) Ortega Aramburu, Joaquín M. |
Keywords: | Anàlisi funcional Espais de Sobolev Equacions en derivades parcials Equacions diferencials el·líptiques Functional analysis Sobolev spaces Partial differential equations Elliptic differential equations |
Issue Date: | 2020 |
Publisher: | Walter de Gruyter |
Abstract: | 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 $H_s^2(\R^n)$. |
Note: | Reproducció del document publicat a: https://doi.org/10.1515/forum-2019-0311/html |
It is part of: | Forum Mathematicum, 2020, vol. 32, num. 4, p. 995-1026 |
URI: | http://hdl.handle.net/2445/193292 |
Related resource: | https://doi.org/10.1515/forum-2019-0311/html |
ISSN: | 0933-7741 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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