Special Session 89: Partial Differential Equations: Diverse Applications and Connections

Global boundedness of solutions to fully anisotropic variational problems
Angela Alberico
Italian National Research Council - Institute for Applied Calculus (Napoli)
Italy
Co-Author(s):    
Abstract:
A class of nonlinear, fully anisotropic variational problems whose anisotropy is governed by a general $n$-dimensional convex function of the gradient is analyzed. Global boundedness for both solutions to fully anisotropic nonlinear elliptic Dirichlet problems, and minima of fully anisotropic variational integrals, is established under general growth conditions, not necessarily of power type. The results unify and extend several existing contributions in the literature, yielding new regularity conclusions across a variety of anisotropic frameworks.