Critical regularity for elliptic equations from Littlewood-Paley theory

2005/06/12 by Denis A. Labutin, Labutin, Denis A.
Mathematics · #35J60 #58J05 #58J40 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35J60 #msc:58J05 #msc:58J40

paper · pdf · doi:10.48550/arxiv.math/0506225

arxiv created 2005/06/12 · arxiv updated 2009/12/01

Abstract

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

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