Morrey Regularity of Nonlinear Elliptic Systems of High Order under Degeneration of Ellipticity

E. A. Kalita

Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 198-206

Résumé

We study nonlinear elliptic systems of the form $\operatorname {div}^tA(x,D^su)=0$, $s+t$ even, $x\in \Omega \subset \mathbb R^n$, with the natural energy space $H^s$. We establish that for $s>t$ solutions from $H^s$ belong to the Morrey space and the Morrey exponent does not tend to zero under the degeneration of ellipticity. In the case $s=t$, a similar result is obtained under an additional structure condition on the system.