Uniform Bounds for the Best Sobolev Trace Constant-Reference-Cited by-同舟云学术

Uniform Bounds for the Best Sobolev Trace Constant

Published:2003-05-01 Issue:2 Volume:3 Page:181-192
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Bonder Julián Fernández¹,Rossi Julio D.²³,Ferreira Raúl⁴⁵

Affiliation:

1. Departamento de Matemática, Universidad de Buenos Aires Ciudad Universitaria (1428), Buenos Aires, Argentina

2. Departamento de Matemáitica Universidad de Buenos Aires Ciudad Universitaria (1428), Buenos Aires, Argentina

3. Departamento de Matemática, Universidad Católica, Casilla 306, correo 22, Santiago, Chile

4. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, España

5. Departamento de Matemáticas, U. Carlos III de Madrid, 28911 Legans, Spain

Abstract

Abstract We study the Sobolev trace embedding W1,p(Ω) ↪ Lq(∂Ω), looking at the dependence of the best constant and the extremals on p and q. We prove that there exists a uniform bound (independent of (p, q)) for the best constant if and only if (p, q) lies far from (N, ∞). Also we study some limit cases, q = ∞ with p > N or p = ∞ with 1 ≤ q ≤ ∞.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2003-0202/pdf

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