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- W2011176504 abstract "In this paper we are concerned with the regularity of minimizers u∈W1,p(Ω,RN) of quasi-convex integral functionals of the typeF[u]:=∫Ωf(x,u,Du)dx. The crucial point here is that the integrand f admits very weak regularity properties. With respect to the gradient variable it satisfies degenerate/singular p-growth conditions without necessarily possessing a quasi-diagonal Uhlenbeck-type structure, and with respect to the x-variable the integrand might be even discontinuous. It is only assumed that a certain VMO-condition holds. Under those assumptions we prove partial Hölder continuity of minimizers, i.e. Hölder continuity of u for any Hölder exponent α∈(0,1) outside a set of measure zero. Under such weak assumptions regularity results for the gradient of minimizers is not expected to hold since even in the scalar case counterexamples to C1-regularity are known." @default.
- W2011176504 created "2016-06-24" @default.
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- W2011176504 date "2012-01-01" @default.
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- W2011176504 title "Partial regularity for minimizers of discontinuous quasi-convex integrals with degeneracy" @default.
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- W2011176504 doi "https://doi.org/10.1016/j.jde.2011.09.031" @default.
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