We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kindSigma(s)(i=1)partial derivative(ii)u Sigma(N)(i=1s+1)partial derivative(i)(A(i)(x, u, del u)) = 0, x is an element of Omega subset of subset of R-N for 1 <= s <= (N -1),where each operator A(i) behaves directionally as the singular p-Laplacian, 1 < p < 2. Throughout a parabolic approach to expansion of positivity we obtain the interior Holder continuity and some integral and pointwise Harnack inequalities.
Simone Ciani, Igor I. Skrypnik, Vincenzo Vespri (2023). On the local behavior of local weak solutions to some singular anisotropic elliptic equations. ADVANCES IN NONLINEAR ANALYSIS, 12(1), 237-265 [10.1515/anona-2022-0275].
On the local behavior of local weak solutions to some singular anisotropic elliptic equations
Simone Ciani
;
2023
Abstract
We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kindSigma(s)(i=1)partial derivative(ii)u Sigma(N)(i=1s+1)partial derivative(i)(A(i)(x, u, del u)) = 0, x is an element of Omega subset of subset of R-N for 1 <= s <= (N -1),where each operator A(i) behaves directionally as the singular p-Laplacian, 1 < p < 2. Throughout a parabolic approach to expansion of positivity we obtain the interior Holder continuity and some integral and pointwise Harnack inequalities.| File | Dimensione | Formato | |
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