Geodesic
Morrey Regularity of Nonlinear Elliptic Systems of High Order under Degeneration of Ellipticity
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 198-206

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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. 
@article{MZM_2002_72_2_a3,
     author = {E. A. Kalita},
     title = {Morrey {Regularity} of {Nonlinear} {Elliptic} {Systems} of {High} {Order} under {Degeneration} of {Ellipticity}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {198--206},
     publisher = {mathdoc},
     volume = {72},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a3/}
}
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E. A. Kalita. Morrey Regularity of Nonlinear Elliptic Systems of High Order under Degeneration of Ellipticity. Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 198-206. http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a3/