Fundamental Solutions and Mapping Properties of Semielliptic Operators

Details Fundamental Solutions and Mapping Properties of Semielliptic Operators Fundamental Solutions and Mapping Properties of Semielliptic Operators

2004-06-09

arxiv.org/abs/math/0406202v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

An explicit formula is given for a fundamental solution for a class of semielliptic operators. The fundamental solution is used to investigate properties of these operators as mappings between weighted function spaces. Necessary and sufficient conditions are given for such a mapping to be an isomorphism. Results apply, for example, to elliptic, parabolic, and generalized p-parabolic operators.

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