论文标题
具有零顺序内核积分方程的经典解决方案
Classical solutions to integral equations with zero order kernels
论文作者
论文摘要
我们显示了全局和内部高阶Log-Hölder规律性估算的DIRICHLET积分方程解决方案，其中操作员具有不可整合的核，其原点的奇异性比任何分数laplacian的核心都弱。结果，在右侧的轻度规律性假设下，我们显示了涉及对数laplacian和对数Schrödinger操作员的迪里奇特问题的经典解决方案。
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.
