New York Journal of Mathematics
Volume 5 (1999) 83-90


Norbert Hungerbühler

Quasilinear Elliptic Systems in Divergence Form with Weak Monotonicity

Published: June 17, 1999
Keywords: Quasilinear elliptic systems, monotone operators, Young measures
Subject: 35J65, 47H15

We consider the Dirichlet problem for the quasilinear elliptic system
-divσ(x,u(x),Du(x))=f on Ω
u(x)=0 on \partialΩ
for a function u:Ω→Rm, where Ω is a bounded open domain in Rn. For arbitrary right hand side f∈ W-1,p'(Ω) we prove existence of a weak solution under classical regularity, growth and coercivity conditions, but with only very mild monotonicity assumptions.

Author information

Max-Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, 04103 Leipzig (Germany)