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On coercive variational integrals

Abstract:

It is well-known that sequential weak lower semicontinuity of a variational integral

𝕱(u, Ω) = βˆ«β„¦ F (βˆ‡u(x)) dx

on the Sobolev space W^1,p (Ω, ℝ^N) under a p-growth condition on the integrand F is equivalent to quasiconvexity in the sense of Morrey. We show that coercivity on Dirichlet classes likewise is equivalent to a quasiconvexity condition. We also discuss more general notions of coercivity, and in the case of positively p-homogeneous integrands F we establish the existe...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1016/j.na.2016.09.011

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Department:
Oxford, MPLS, Mathematical Institute
Publisher:
Elsevier Publisher's website
Journal:
Nonlinear Analysis Theory Methods and Applications Journal website
Volume:
153
Pages:
213–229
Publication date:
2016-10-05
Acceptance date:
2016-09-16
DOI:
ISSN:
0362-546X
Pubs id:
pubs:656463
URN:
uri:fcfa67ba-95bd-46fa-9341-ea623611420b
UUID:
uuid:fcfa67ba-95bd-46fa-9341-ea623611420b
Local pid:
pubs:656463

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