Existence and Lipschitz Regularity for Minima (original) (raw)
Proceedings of the American Mathematical Society
We prove the existence, uniqueness and Lipschitz regularity of the minima of the integral functional I(u )= Z L(x;u;ru)dx on u + W 1;q 0 () (1 q +1) 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.
Sign up for access to the world's latest research.
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Related papers
A boundary regularity result for minimizers of variational integrals with nonstandard growth
Nonlinear Analysis, 2018
We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in W 1,1 with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example bounded slope condition). Furthermore, we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains. The result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions.
Regularity results for minimizers of irregular integrals with (p,q) growth
Forum Mathematicum, 2000
We consider variational integrals f Du dx where u X 3 R N and the convex function f has pY q growth jzj p f z Ljzj q 1, p`q. We prove local Lipschitz continuity of minimizers in the scalar case and in some vectorial cases. We further prove higher integrability and di¨erentiability for local minimizers. The results cover the case in which f is degenerate convex. A main feature of the paper is that we do not assume that f is di¨erentiable everywhere.
Regularity results for vectorial minimizers of a class of degenerate convex integrals
Journal of Differential Equations
We establish the higher differentiability and the higher integrability for the gradient of vectorial minimizers of integral functionals with (p, q)-growth conditions. We assume that the nonhomogeneous densities are uniformly convex and have a radial structure, with respect to the gradient variable, only at infinity. The results are obtained under a possibly discontinuous dependence on the spatial variable of the integrand.
Lipschitz minimizers for a class of integral functionals under the bounded slope condition
arXiv (Cornell University), 2020
We consider the functional Ω g(∇u + X *) dL 2n where g is convex and X * (x, y) = 2(−y, x) and we study the minimizers in BV(Ω) of the associated Dirichlet problem. We prove that, under the bounded slope condition on the boundary datum, and suitable conditions on g, there exists a unique minimizer which is also Lipschitz continuous.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.