We study equations in divergence form with piecewise $C^{\alpha }$ coefficients. The domains contain corners and the discontinuity surfaces are attached to the edges of the corners. We obtain piecewise $C^{1,\alpha }$ estimates across the discontinuity surfaces and provide an example to illustrate the issue regarding the regularity at the corners.
Jun Chen
,
Xuemei Deng
. ELLIPTIC EQUATIONS IN DIVERGENCE FORM WITH DISCONTINUOUS COEFFICIENTS IN DOMAINS WITH CORNERS*[J]. Acta mathematica scientia, Series B, 2024
, 44(5)
: 1903
-1915
.
DOI: 10.1007/s10473-024-0515-2
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