2025/04/05 by Irene Gonzálvez, Gonzálvez, Irene, Fernando Quirós +4 · 2 citations
Mathematics · #35A01 #35A02 #35C15 #35K08 #35S05 #60J60 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2504.04246
openalex publication_date 2025/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop a Widder-type theory for nonlocal heat equations involving quite general Lévy operators. Thus, we consider nonnegative solutions and look for conditions on the operator that ensure: (i) uniqueness of nonnegative classical and very weak solutions with a given initial trace; (ii) the existence of an initial trace, belonging to certain admissibility class; and (iii) the existence of a solution, given by a representation formula, for any admissible initial trace. Such results are obtained first for purely nonlocal Lévy operators defined through positive symmetric Lévy kernels comparable to radial functions with mixed polynomial growth, and then extended to more general operators, including anisotropic ones and operators that have both a local and a nonlocal part.