Abstract
Hölder continuity of solutions is proved for a new class of degenerate divergent second-order elliptic equations with weight not satisfying the Muckenhoupt condition. There is no Harnack inequality and no Sobolev embedding theorems with higher summation exponent for these equations. As an example an equation is considered in a domain divided into two parts by a hyperplane. In each part the weight function is a power one, the powers are different, and their absolute values do not exceed the space dimension.
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Alkhutov, Y.A., Zhikov, V.V. A Class of Degenerate Elliptic Equations. Journal of Mathematical Sciences 120, 1247–1254 (2004). https://doi.org/10.1023/B:JOTH.0000016047.98038.8d
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DOI: https://doi.org/10.1023/B:JOTH.0000016047.98038.8d