Abstract
We study nonlinear elliptic systems of the form \({\text{div}}^t A(x,D^s u) = 0\), \(s + t\) 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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REFERENCES
C. B. Morrey, “On the solutions of quasi-linear elliptic partial differential equations,” Trans. Amer. Math. Soc., 43 (1938), 126–166.
K.-O. Widman, “Hölder continuity of solutions of elliptic systems,” Manuscr. Math., 5 (1971), no. 4, 299–308.
V. A. Solonnikov, “On the differential properties of weak solutions of quasilinear elliptic equations,” Zapiski Nauchn. Sem. LOMI, 39 (1974), 110–119.
H. O. Cordes, “Zero order a priori estimates for solutions of elliptic differential equations,” Proc. Symp. Pure Math., 4 (1961), 157–166.
E. M. Dyn'kin and B. P. Osilenker, “Weighted estimates of singular integrals and their applications,” in: Itogi Nauki i Tekhniki. Mat. Analiz, vol. 21, VINITI, Moscow, 1983, pp. 42–129.
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Kalita, E.A. Morrey Regularity of Nonlinear Elliptic Systems of High Order under Degeneration of Ellipticity. Mathematical Notes 72, 177–184 (2002). https://doi.org/10.1023/A:1019841726745
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DOI: https://doi.org/10.1023/A:1019841726745