Self-improving properties for a class of elliptic and parabolic equations on bounded domains

Tadele Mengesha; Abner J. Salgado

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arXiv · 2606.06677

Self-improving properties for a class of elliptic and parabolic equations on bounded domains

Tadele Mengesha·Abner J. Salgado

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Abstract

We discuss self improving properties of some local and nonlocal, elliptic and parabolic, equations on bounded domains. We employ a functional analytic approach wherein the solution space sits in a suitable interpolation scale. Utilizing a classical analytic perturbation result, we extrapolate the invertibility of the main operator from the base space to nearby spaces within the interpolation family.

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Tadele Mengesha, Abner J. Salgado. 2026-06-04. Self-improving properties for a class of elliptic and parabolic equations on bounded domains. https://arxiv.org/abs/2606.06677

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