Well-posedness of Tricomi-Gellerstedt-Keldysh-type fractional elliptic problems

TL;DR

This paper investigates the well-posedness of fractional elliptic boundary value problems of Tricomi-Gellerstedt-Keldysh type, providing results applicable to various domains and operators with positive spectrum.

Contribution

It establishes well-posedness results for a broad class of fractional elliptic problems with general positive operators and Fourier multipliers, extending previous work to new domain configurations.

Findings

Well-posedness results for fractional elliptic problems on diverse domains

Applicability to operators with discrete spectrum and positive symbols

Analysis includes half-cylinder, star-shaped graph, and half-space domains

Abstract

In this paper Tricomi-Gellerstedt-Keldysh-type fractional elliptic equations are studied. The results on the well-posedness of fractional elliptic boundary value problems are obtained for general positive operators with discrete spectrum and for Fourier multipliers with positive symbols. As examples, we discuss results in half-cylinder, star-shaped graph, half-space and other domains.