Existence and Regularity of Minimizers of Nonconvex Functionals Depending onuand ∇u

Autor:	Pietro Celada
Rok vydání:	1999
Předmět:	Quadratic growth Hölder's inequality Convex hull Sobolev space Pure mathematics Epigraph Applied Mathematics Mathematical analysis Lipschitz continuity Nonconvex minimum problems existence and regularity of solutions Analysis Mathematics
Zdroj:	Journal of Mathematical Analysis and Applications. 230(1):30-56
ISSN:	0022-247X
DOI:	10.1006/jmaa.1998.6163
Popis:	We consider variational problems of the form min ∫ Ω [f(Δu(x)) + g(x, u(x))]dx: u ∈ u 0 + H 1 0 (Ω) , wheref: R N → [0, ∞] is a possibly nonconvex function with quadratic growth at infinity andg(x, u) is Lipschitz continuous and strictly increasing (decreasing) inu. We prove the existence and local Lipschitz regularity of solutions for every boundary datumu0 ∈ H1(Ω) ∩ L∞(Ω) on the basis of the structure of the epigraph of the convex envelope off.
Databáze:	OpenAIRE
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