Geodesic
THE BEST SOBOLEV TRACE CONSTANT IN PERIODIC MEDIA FOR CRITICAL AND SUBCRITICAL EXPONENTS
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 619-630

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DOI

In this paper we study homogenisation problems for Sobolev trace embedding H1(Ω) ↪ Lq(∂Ω) in a bounded smooth domain. When q = 2 this leads to a Steklov-like eigenvalue problem. We deal with the best constant of the Sobolev trace embedding in rapidly oscillating periodic media, and we consider H1 and Lq spaces with weights that are periodic in space. We find that extremals for these embeddings converge to a solution of a homogenised limit problem, and the best trace constant converges to a homogenised best trace constant. Our results are in fact more general; we can also consider general operators of the form aɛ(x, ∇u) with non-linear Neumann boundary conditions. In particular, we can deal with the embedding W1,p(Ω) ↪ Lq(∂Ω).
DOI : 10.1017/S0017089509990048
Mots-clés : 35B27, 35J65, 46E35 
BONDER, JULIÁN FERNÁNDEZ; ORIVE, RAFAEL; ROSSI, JULIO D. THE BEST SOBOLEV TRACE CONSTANT IN PERIODIC MEDIA FOR CRITICAL AND SUBCRITICAL EXPONENTS. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 619-630. doi: 10.1017/S0017089509990048
@article{10_1017_S0017089509990048,
     author = {BONDER, JULI\'AN FERN\'ANDEZ and ORIVE, RAFAEL and ROSSI, JULIO D.},
     title = {THE {BEST} {SOBOLEV} {TRACE} {CONSTANT} {IN} {PERIODIC} {MEDIA} {FOR} {CRITICAL} {AND} {SUBCRITICAL} {EXPONENTS}},
     journal = {Glasgow mathematical journal},
     pages = {619--630},
     year = {2009},
     volume = {51},
     number = {3},
     doi = {10.1017/S0017089509990048},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990048/}
}
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