Geodesic
Anisotropic nonlocal diffusion equations with singular forcing
de Pablo, Arturo1 ; Quirós, Fernando2 ; Rodríguez, Ana3
1 Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
3 Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1167-1183

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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.

DOI : 10.1016/j.anihpc.2020.04.001
Classification : 35R11, 35B65, 35A05
Keywords: Non-local diffusion, Anisotropic stable operators, Well-posedness, Regularity, Singular forcing, Heat kernel estimates for Lévy processes

de Pablo, Arturo 1 ; Quirós, Fernando 2 ; Rodríguez, Ana 3

1 Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911 Leganés, Spain
2 Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
3 Departamento de Matemática Aplicada, Universidad Politécnica de Madrid, 28040 Madrid, Spain 
@article{AIHPC_2020__37_5_1167_0,
     author = {de Pablo, Arturo and Quir\'os, Fernando and Rodr{\'\i}guez, Ana},
     title = {Anisotropic nonlocal diffusion equations with singular forcing},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1167--1183},
     publisher = {Elsevier},
     volume = {37},
     number = {5},
     year = {2020},
     doi = {10.1016/j.anihpc.2020.04.001},
     mrnumber = {4138230},
     zbl = {1454.35411},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.04.001/}
}
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de Pablo, Arturo; Quirós, Fernando; Rodríguez, Ana. Anisotropic nonlocal diffusion equations with singular forcing. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 5, pp. 1167-1183. doi: 10.1016/j.anihpc.2020.04.001

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