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On the interior smoothness of solutions to second-order elliptic equations. (Russian, English) Zbl 1114.35037
Sib. Mat. Zh. 46, No. 5, 1036-1052 (2005); translation in Sib. Math. J. 46, No. 5, 826-840 (2005).
Summary: We study the interior smoothness properties of solutions to a linear second-order uniformly elliptic equation in selfadjoint form without lower-order terms and with measurable bounded coefficients. In terms of membership in a special function space we combine and supplement some properties of solutions such as membership in the Sobolev space \(W^1_{2,\text{loc}}\) and Hölder continuity. We show that the membership of solutions in the introduced space which we establish in this article gives some new properties that do not follow from Hölder continuity and the membership in \(W^1_{2,\text{loc}}\).

35B65 Smoothness and regularity of solutions to PDEs
35J15 Second-order elliptic equations
35R05 PDEs with low regular coefficients and/or low regular data
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