Critical regularity for elliptic equations from Littlewood-Paley theory

Denis A. Labutin

Critical regularity for elliptic equations from Littlewood-Paley theory

Analysis of PDEs 2007-05-23 v1 Differential Geometry

Authors: Denis A. Labutin

Abstract

Using simple facts from harmonic analysis, namely Bernstein inequality and Plansherel isometry, we prove that the pseudodifferential equation $\Delta^\alpha u+Vu=0$ improves the Sobolev regularity of solutions provided the potential $V$ is integrable with the critical power $n/2\alpha>1$ .

Keywords

semilinear elliptic equations singular solutions of pdes sobolev regularity of partial differential equations

Cite

@article{arxiv.math/0506225,
  title  = {Critical regularity for elliptic equations from Littlewood-Paley theory},
  author = {Denis A. Labutin},
  journal= {arXiv preprint arXiv:math/0506225},
  year   = {2007}
}

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