We consider a map $u:\mathbb{R}^{n}\to \mathbb{R}^{m}$ , $n,m>1$ solution to a nonlinear systems of partial differential equations, or minimizer of a functional of the calculus of variations. It is well known that either the global or the local boundedness of $u$ cannot be obtained through truncation methods. This is due to the lack of maximum principles for general systems. Nevertheless in this paper we present a method for local boundedness of $u$ without assuming any condition on the boundary datum.

Local boundedness of solutions to some anisotropic elliptic systems

CUPINI, GIOVANNI;
2013

Abstract

We consider a map $u:\mathbb{R}^{n}\to \mathbb{R}^{m}$ , $n,m>1$ solution to a nonlinear systems of partial differential equations, or minimizer of a functional of the calculus of variations. It is well known that either the global or the local boundedness of $u$ cannot be obtained through truncation methods. This is due to the lack of maximum principles for general systems. Nevertheless in this paper we present a method for local boundedness of $u$ without assuming any condition on the boundary datum.
2013
RECENT TRENDS IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS II: STATIONARY PROBLEMS
169
186
G. Cupini; P. Marcellini; E. Mascolo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/181482
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