Fundamental solution for Cauchy initial value problem for parabolic PDEs\n with discontinuous unbounded first-order coefficient at the origin. Extension\n of the classical parametrix method

2019/06/13 by Maria Rosaria Formica, Formica, Maria Rosaria, Eugeny Ostrovsky +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1906.05880

openalex publication_date 2019/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the existence of a fundamental solution of the Cauchy initial\nboundary value problem on the whole space for a parabolic partial differential\nequation with discontinuous unbounded first-order coefficient at the origin. We\nestablish also non-asymptotic, rapidly decreasing at infinity, upper and lower\nestimates for the fundamental solution. We extend the classical parametrix\nmethod provided by E.E. Levi.\n

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