On the role of Riesz potentials in Poisson's equation and Sobolev embeddings

DOI10.1512/IUMJ.2015.64.5706zbMath1338.31011arXiv1404.1563OpenAlexW2476701487MaRDI QIDQ2788635

Rahul Garg, Daniel E. Spector

Publication date: 22 February 2016

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1404.1563

zbMATH Keywords

Sobolev embeddingsPoisson's equationRiesz potentials

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (8)

Best constants for two families of higher order critical Sobolev embeddings ⋮ On the Hölder regularity for the fractional Schrödinger equation and its improvement for radial data ⋮ A trace inequality for solenoidal charges ⋮ On the regularity of solutions to Poisson's equation ⋮ New directions in harmonic analysis on \(L^1\) ⋮ An \(L^1\)-type estimate for Riesz potentials ⋮ Sharp pointwise gradient estimates for Riesz potentials with a bounded density ⋮ An improvement to the John-Nirenberg inequality for functions in critical Sobolev spaces

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