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Pseudodifferential Operators with Symbols in Weighted Sobolev Spaces and Regularity for non Linear Partial Differential Equations
Author(s) -
Garello Gianluca
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200206)239:1<62::aid-mana62>3.0.co;2-w
Subject(s) - mathematics , pseudodifferential operators , sobolev space , pointwise , partial differential equation , pure mathematics , operator (biology) , lipschitz continuity , multiplication (music) , partial derivative , mathematical analysis , combinatorics , biochemistry , chemistry , repressor , transcription factor , gene
We obtain a result of continuity for pseudodifferential operator whose symbols belong to fully inhomogeneous weighted Sobolev spaces, which realize moreover to be algebras with respect to the pointwise multiplication. Applications to the study of the local regularity for some classes of non linear partial differential equations are given, besides some remarks about a number of weight functions which appear in the literature related to the weighted pseudodifferential calculus.