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. 
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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/

[1] Morrey C. B., “On the solutions of quasi-linear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43 (1938), 126–166 | DOI | MR | Zbl

[2] Widman K.-O., “Hölder continuity of solutions of elliptic systems”, Manuscr. Math., 5:4 (1971), 299–308 | DOI | MR | Zbl

[3] Solonnikov V. A., “O differentsialnykh svoistvakh slabykh reshenii kvazilineinykh ellipticheskikh uravnenii”, Zapiski nauch. sem. LOMI, 39, Nauka, L., 1974, 110–119 | MR | Zbl

[4] Cordes H. O., “Zero order a priori estimates for solutions of elliptic differential equations”, Proc. Symp. Pure Math., 4, 1961, 157–166 | MR | Zbl

[5] Dynkin E. M., Osilenker B. P., “Vesovye otsenki singulyarnykh integralov i ikh prilozheniya”, Itogi nauki i tekhniki. Matem. analiz, 21, VINITI, M., 1983, 42–129 | MR