Time fractional parabolic equations with measurable coefficients and embeddings for fractional parabolic Sobolev spaces

2021/03/05 by Hongjie Dong, Dong, Hongjie, Doyoon Kim +1 · 1 citation
Mathematics · #26A33 #35R05 #35R11 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2103.03410

openalex publication_date 2021/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider time fractional parabolic equations in both divergence and non-divergence form when the leading coefficients a^ij are measurable functions of (t,x₁) except for a¹¹ which is a measurable function of either t or x₁. We obtain the solvability in Sobolev spaces of the equations in the whole space, on a half space, or on a partially bounded domain. The proofs use a level set argument, a scaling argument, and embeddings in fractional parabolic Sobolev spaces for which we give a direct and elementary proof.

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