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The best Sobolev trace constant in periodic media for critical and subcritical exponents
(Cambridge University Press, 2009-09)
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 ...
On the Sobolev trace Theorem for variable exponent spaces in the critical range
(Springer Heidelberg, 2013-05)
In this paper, we study the Sobolev trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then, we give local conditions ...
The best Sobolev trace constant in domains with holes for critical or subcritical exponents
(Cambridge University Press, 2007-12)
In this paper we study the best constant in the Sobolev trace embedding H1 (Ω) → Lq(∂Ω) in a bounded smooth domain for 1 < q ≤ 2+ = 2(N - 1)/(N - 2), that is, critical or subcritical q. First, we consider a domain with ...
Optimization problem for extremals of the trace inequality in domains with holes
(World Scientific, 2010-08)
We study the Sobolev trace constant for functions defined in a bounded domain Ω that vanish in the subset A. We find a formula for the first variation of the Sobolev trace with respect to the hole. As a consequence of this ...
On the existence of extremals for the Sobolev trace embedding theorem with critical exponent
(WILEY, 2005)
In this paper, the existence problem is studied for extremals of the Sobolev trace inequality W-1,W-p(Omega) --> L-p* (partial derivativeOmega), where Omega is a bounded smooth domain in R-N, p(*) = p(N - 1)/(N - p) is the ...
The best Sobolev trace constant in a domain with oscillating boundary
(Pergamon-Elsevier Science Ltd, 2007-12)
In this paper we study homogenization problems for the best constant for the Sobolev trace embedding W1, p (Ω) {right arrow, hooked} Lq (∂ Ω) in a bounded smooth domain when the boundary is perturbed by adding an oscillation. ...
Symmetry properties for the extremals of the Sobolev trace embedding
(Gauthier-Villars/Editions Elsevier, 2004-11)
In this article we study symmetry properties of the extremals for the Sobolev trace embedding H1(B(0, µ)) ,→ Lq(∂B(0, µ)) with 1 ≤ q ≤2(N − 1)/(N − 2) for different values of µ. These extremals u are solutions of the problem ...
Existence of solution to a critical trace equation with variable exponent
(IOS Press, 2015-06)
In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the p(x)-Laplacian where the critical term is placed as a source through the boundary of the domain. ...
Funciones de Sobolev y Besov en espacios métricos
(2015-03-09)
En el contexto abstracto de espacios métricos con medida varios autores han considerado espacios de funciones de regularidad tipo Lipschitz o Besov con orden de suavidad alfa menor a uno. Para el extremo alfa igual a uno, ...