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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:
It is part of: Forum Mathematicum, 2020, vol. 32, num. 4, p. 995-1026
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ISSN: 0933-7741
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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