We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional I(u) = integral (Omega) L(x, u, delu) dx on (u) over bar + W-0(1,q)(Omega) (1 less than or equal to q less than or equal to +infinity) for a class of integrands L(x, z, p) = f(p) + g(x, z) that are convex in (z, p) and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on L.
Existence and Lipschitz regularity for minima
MARICONDA, CARLO;TREU, GIULIA
2002
Abstract
We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional I(u) = integral (Omega) L(x, u, delu) dx on (u) over bar + W-0(1,q)(Omega) (1 less than or equal to q less than or equal to +infinity) for a class of integrands L(x, z, p) = f(p) + g(x, z) that are convex in (z, p) and for boundary data satisfying some barrier conditions. We do not impose regularity or growth assumptions on L.File in questo prodotto:
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