Lower semicontinuous envelopes in W^{1,1}xL^p

Ana Margarida Fernandes Ribeiro

doi:10.4064/bc101-0-15

Lower semicontinuous envelopes in W^{1,1}xL^p

Ana Margarida Fernandes Ribeiro

DM - Departamento de Matemática

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

It is studied the lower semicontinuity of functionals of the type \int_{\Omega} f(x, u, v,\nabla u)dx with respect to the (W^{1,1} \times L^p)-weak*topology. Moreover in absence of lower semicontinuity, it is also provided an integral representation in W^{1,1}\times L^p for the lower semicontinuous envelope.

Original language	Unknown
Title of host publication	Banach Center Publications
Pages	187-206
DOIs	https://doi.org/10.4064/bc101-0-15
Publication status	Published - 1 Jan 2014
Event	Calculus of Variations and PDEs - Duration: 1 Jan 2012 → …

Conference

Conference	Calculus of Variations and PDEs
Period	1/01/12 → …

Access to Document

10.4064/bc101-0-15

Cite this

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title = "Lower semicontinuous envelopes in W^{1,1}xL^p",

abstract = "It is studied the lower semicontinuity of functionals of the type \int_{\Omega} f(x, u, v,\nabla u)dx with respect to the (W^{1,1} \times L^p)-weak*topology. Moreover in absence of lower semicontinuity, it is also provided an integral representation in W^{1,1}\times L^p for the lower semicontinuous envelope.",

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N2 - It is studied the lower semicontinuity of functionals of the type \int_{\Omega} f(x, u, v,\nabla u)dx with respect to the (W^{1,1} \times L^p)-weak*topology. Moreover in absence of lower semicontinuity, it is also provided an integral representation in W^{1,1}\times L^p for the lower semicontinuous envelope.

AB - It is studied the lower semicontinuity of functionals of the type \int_{\Omega} f(x, u, v,\nabla u)dx with respect to the (W^{1,1} \times L^p)-weak*topology. Moreover in absence of lower semicontinuity, it is also provided an integral representation in W^{1,1}\times L^p for the lower semicontinuous envelope.

KW - lower semicontinuity

KW - convexity-quasiconvexity

U2 - 10.4064/bc101-0-15

DO - 10.4064/bc101-0-15

M3 - Conference contribution

SN - 978-83-86806-23-2

SP - 187

EP - 206

BT - Banach Center Publications

Y2 - 1 January 2012

ER -