Classical solutions to integral equations with zero order kernels
HA Chang-Lara, A Saldaña - Mathematische Annalen, 2024 - Springer
Mathematische Annalen, 2024•Springer
We show global and interior higher-order log-Hölder regularity estimates for solutions of
Dirichlet integral equations where the operator has a nonintegrable kernel with a singularity
at the origin that is weaker than that of any fractional Laplacian. As a consequence, under
mild regularity assumptions on the right hand side, we show the existence of classical
solutions of Dirichlet problems involving the logarithmic Laplacian and the logarithmic
Schrödinger operator.
Dirichlet integral equations where the operator has a nonintegrable kernel with a singularity
at the origin that is weaker than that of any fractional Laplacian. As a consequence, under
mild regularity assumptions on the right hand side, we show the existence of classical
solutions of Dirichlet problems involving the logarithmic Laplacian and the logarithmic
Schrödinger operator.
Abstract
We show global and interior higher-order log-Hölder regularity estimates for solutions of Dirichlet integral equations where the operator has a nonintegrable kernel with a singularity at the origin that is weaker than that of any fractional Laplacian. As a consequence, under mild regularity assumptions on the right hand side, we show the existence of classical solutions of Dirichlet problems involving the logarithmic Laplacian and the logarithmic Schrödinger operator.
Springer
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