A mapping property of the heat volume potential

TL;DR

This paper investigates the mapping properties of the heat volume potential in distribution spaces related to time derivatives of H"older functions, and applies these results to solve boundary value problems for the heat equation with non-homogeneous terms.

Contribution

It establishes new mapping properties of the heat volume potential in distribution spaces and applies them to solve Dirichlet and Neumann problems for the heat equation.

Findings

Proved a new mapping property of the heat volume potential.

Solved Dirichlet and Neumann problems with non-homogeneous terms.

Extended the theory of heat potentials to distribution spaces.

Abstract

We consider the volume potential associated with the heat operator and we prove a mapping property in the space of distributions which are the time derivative of H\"older continuous functions. As an application we solve the Dirichlet and Neumann problems for the heat equation with a non-homogeneous term in such space of distributions.