What question did this study set out to answer?

This research aims to clarify Brezis–Browder type results for s-harmonic functions and their relation to the fractional Poisson’s equation.

March 14, 2026

Elementary Brezis–Browder type results and representation formulae for 𝑠-harmonic functions

Key Points

This research aims to clarify Brezis–Browder type results for s-harmonic functions and their relation to the fractional Poisson’s equation.
Proved results for fractional Sobolev spaces
Evaluated s-harmonic functions
Established sufficient conditions for solutions to Poisson’s equation
Demonstrated that distributional solutions to fractional Poisson’s equation can be represented in terms of an integral
Identified the quantitative type estimates for s-harmonic functions

Abstract

We prove Brezis–Browder type results for fractional Sobolev spaces and quantitative type estimates for s s –harmonic functions. Furthermore, we give sufficient conditions for distributional solutions to the fractional Poisson’s equation (− Δ) s u = T (-) ˢu=T on R d Rᵈ to be of the form u (x) = ∫ R d T (y) | x − y | d − 2 s d y + l, l ∈ R. equation* u (x) = ₑᵈ T (y) |x-y|^{d-2s}dy+l, l R. equation*

AI से पूछें

Bookmark

Cite This Study

Damiano Greco (Wed,) studied this question.

synapsesocial.com/papers/69b4ad8d18185d8a39801024 https://doi.org/https://doi.org/10.1090/proc/17504

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

AI से पूछें

Bookmark