Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner | Zendy

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Trace Theorems for Anisotropic Weighted SOBOLEV Spaces in a Corner

Author(s) -

Franchi Bruno

Publication year - 1986

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/mana.19861270104

Subject(s) - mathematics , sobolev space , trace class , trace (psycholinguistics) , euclidean geometry , pure mathematics , sobolev inequality , trace operator , class (philosophy) , degenerate energy levels , elliptic operator , operator (biology) , mathematical analysis , geometry , boundary value problem , philosophy , repressor , artificial intelligence , linguistics , chemistry , computer science , biochemistry , hilbert space , quantum mechanics , transcription factor , free boundary problem , elliptic boundary value problem , physics , gene

In this paper, we prove a trace theorem for anisotropic weighted Sobolev spaces in a cube Q naturally associated to a class of degenerate elliptic operators. The fundamental property of this class is the existence of a suitable metric d which is “natural” for the operators. The basic tool of the proof is a representation formula obtained via suitable non‐euclidean translations closely fitting the geometry of the d ‐balls. In a more particular situation, we construct a right inverse of the trace operator and we describe the compatibility conditions on the edges of Q .

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