Partial regularity of minimizers of asymptotically convex functionals with Morrey coefficients

We consider minimizers of the functional integral(Omega) f(x, u, Du) dx, where f is asymptotically related the function (x, u, xi) bar right arrow a(x,u)G(xi) with G a function with p-Uhlenbeck structure and a is an element of l(0) (Omega x R-N). The main contribution of this article is to refine the growth estimate imposed on f. In particular, we assume that vertical bar f(x, u, xi)vertical bar <= mu(1) (x) + mu(2) (x) vertical bar u vertical bar(s) + M(1 + vertical bar xi vertical bar(2))( p/2), where mu(2) is an element of L-gamma,L-beta (Omega) for some numbers beta and gamma. By assuming only that the coefficient mu(2) belongs to a Morrey space, relative to existing results in the literature we are able to better match our results to a given problem. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This article focuses on minimizers of a functional integral, refining growth estimates by imposing restrictions on the coefficient, which improves the matching of results to specific problems compared to existing literature.