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.
G. Cupini, P. Marcellini, E. Mascolo (2013). Local boundedness of solutions to some anisotropic elliptic systems. PROVIDENCE, RI 02940 USA : American Mathematical Society [10.1090/conm/595/11803].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
