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7552138 
Journal Article 
Existence of free discontinuity problems in SBD(Omega) 
Lu, ZX; Yang, XP 
2009 
1 
Nonlinear Analysis: Theory, Methods & Applications
ISSN: 0362-546X 
PERGAMON-ELSEVIER SCIENCE LTD 
OXFORD 
71 
1-2 
332-340 
WOS:000266225600036 
In this paper, we consider the variational problems for the following two functionals in SBD(Omega): F-1(u) = integral(Omega)f(1)(x, ... u)dx + alpha HN-1(J(u)) + beta integral(integral u)g(x, [u] circle dot v(u))dH(N-1) - integral(Omega)h . udx, F-2(u) = integral(Omega)f(2)(x, u, ... u)dx + alpha HN-1(J(u)) + beta integral(integral u)g(x, [u] circle dot v(u))dH(N-1) - integral(Omega)h . udx where f(1) : Omega x M-sym(NxN) -> [0, infinity) be a Caratheodory function satisfying a weak convexity property and growth assumptions of order s > 1. f(2) and g satisfy convexity property and lower semicontinuity. h is an element of L-P(Omega, R-N), p >= N satisfies the compatibility condition. alpha, beta > 0. Here we do not assume that u(x) is an element of H(x) a.e. in Omega, {H(x)}(x is an element of Omega) be a uniformly bounded family of closed subsets of R-N. (C) 2008 Elsevier Ltd. All rights reserved.