We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very little regularity and that the spectral measure can be singular in some directions. The proofs require having good enough estimates for the corresponding heat kernels and their derivatives.

中文翻译：

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具有奇异强迫的各向异性非局部扩散方程

我们证明了与各向异性稳定扩散算子相关的非局部热方程解的存在性，唯一性和正则性。主要特征是，右侧几乎没有规律性，并且频谱量度在某些方向上可能是奇异的。证明要求对相应的热核及其衍生物具有足够好的估计。