Sobolev and Lipschitz regularity for local minimizers of widely degenerate anisotropic functionals
نویسندگان
چکیده
We prove higher differentiability of bounded local minimizers to some widely degenerate functionals, verifying superquadratic anisotropic growth conditions. In the two dimensional case, we prove that local minimizers to a model functional are locally Lipschitz continuous functions, without any restriction on the anisotropy.
منابع مشابه
Regularity under Sharp Anisotropic General Growth Conditions
We prove boundedness of minimizers of energy-functionals, for instance of the anisotropic type (1.1) below, under sharp assumptions on the exponents pi in terms of p ∗: the Sobolev conjugate exponent of p; i.e., p∗ = np n−p , 1 p = 1 n Pn i=1 1 pi . As a consequence, by mean of regularity results due to Lieberman [21], we obtain the local Lipschitz-continuity of minimizers under sharp assumptio...
متن کاملPartial Sobolev spaces and anisotropic smectic liquid crystals
The partial Sobolev spaces with respect to a vector field are introduced, and are used to studyminimization problems of the functionals which are degenerate in the sense that they do not have control on either the tangential part or the perpendicular part of the magnetic gradients. Based on these results we obtain the asymptotic behavior of the minimizers of the anisotropic Landau-de Gennes fun...
متن کاملEXISTENCE AND REGULARITY OF MINIMIZERS OF NONCONVEX INTEGRALS WITH p− q GROWTH
We show that local minimizers of functionals of the form Z Ω [f(Du(x)) + g(x , u(x))] dx, u ∈ u0 + W 1,p 0 (Ω), are locally Lipschitz continuous provided f is a convex function with p − q growth satisfying a condition of qualified convexity at infinity and g is Lipschitz continuous in u. As a consequence of this, we obtain an existence result for a related nonconvex functional.
متن کاملRegularity of minimizers of a Ginzburg-Landau type energy with metric cone target space
In this paper, we consider an energy of the type Dirichlet energy plus potential term, for a map with values into a metric cone. We investigate the regularity of minimizers of such functionals, and prove that they are always locally Hölder continuous. We establish that Lipschitz continuity is achieved in some cases where the target space has non-positive curvature, and show examples for which t...
متن کاملCongested Traffic Equilibria and Degenerate Anisotropic PDEs
Congested traffic problems on very dense networks lead, at the limit, to minimization problems posed on measures on curves as shown in [2]. Here, we go one step further by showing that these problems can be reformulated in terms of the minimization of an integral functional over a set of vector fields with prescribed divergence. We prove a Sobolev regularity result for their minimizers despite ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016