JournalsaihpcVol. 37, No. 5pp. 1167–1183

Anisotropic nonlocal diffusion equations with singular forcing

  • Ana Rodríguez

    Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain

  • Arturo de Pablo

    Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain

  • Fernando Quirós

    Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Anisotropic nonlocal diffusion equations with singular forcing cover

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Abstract

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.

Cite this article

Ana Rodríguez, Arturo de Pablo, Fernando Quirós, Anisotropic nonlocal diffusion equations with singular forcing. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 5, pp. 1167–1183

DOI 10.1016/J.ANIHPC.2020.04.001