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Variable Exponent Sobolev Spaces and Regularity of Domains
(Springer, 2020)
We study the embeddings of variable exponent Sobolev and Hölder function spaces over Euclidean domains, providing necessary and/or sufficient conditions on the regularity of the exponent and/or the domain in various contexts. ...
A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
(Academic Press Inc Elsevier Science, 2016-10)
In this paper, we study the critical Sobolev embeddings W1,p(.)(Ω)⊂Lp*(.)(Ω) for variable exponent Sobolev spaces from the point of view of the Γ-convergence. More precisely we determine the Γ-limit of subcritical approximation ...
Symmetry and compact embeddings for critical exponents in metric-measure spaces
(Academic Press Inc., 2020-11)
We obtain a compact Sobolev embedding for H-invariant functions in compact metric-measure spaces, where H is a subgroup of the measure preserving bijections. In Riemannian manifolds, H is a subgroup of the volume preserving ...
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 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 Best Constants for Limiting Embeddings of Fractional Sobolev Spaces
(Advanced Nonlinear Studies, IncSan AntonioEUA, 2010)
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 ...
On Newton-Sobolev spaces
(Kossuth Lajos Tudomanyegyetem, 2017-01)
Newton-Sobolev spaces, as presented by N. Shanmugalingam, describe a way to extend Sobolev spaces to the metric setting via upper gradients, for metric spaces with ´sucient´ paths of nite length. Sometimes, as is the case ...
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 ...
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. ...