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- W4313378957 abstract "In this paper we extend the interior regularity results for stable solutions in [Cabré, Figalli, Ros-Oton, and Serra, Acta Math. 224 (2020)] to operators with variable coefficients. We show that stable solutions to the semilinear elliptic equation $ a_{ij}(x)u_{ij} + b_i(x) u_i + f(u) = 0 $ are Hölder continuous in the optimal range of dimensions $ n leq 9 $. Our bounds are independent of the nonlinearity $ f in C^1 $, which we assume to be nonnegative.The main achievement of our work is to make the constants in our estimates depend on the $ C^1 $ norm of $ a_{ij} $ and the $ C^0 $ norm of $ b_i $, instead of their $ C^2 $ and $ C^1 $ norms, respectively, which arise in a first approach to the computations." @default.
- W4313378957 created "2023-01-06" @default.
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- W4313378957 date "2023-01-01" @default.
- W4313378957 modified "2023-10-14" @default.
- W4313378957 title "Stable solutions to semilinear elliptic equations for operators with variable coefficients" @default.
- W4313378957 doi "https://doi.org/10.3934/cpaa.2022162" @default.
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