56 research outputs found
A shape optimization problem for Steklov eigenvalues in oscillating domains
In this paper we study the asymptotic behavior of some optimal design
problems related to nonlinear Steklov eigenvalues, under irregular (but
diffeomorphic) perturbations of the domain.Comment: Some typos fixe
An optimization problem for the first weighted eigenvalue problem plus a potential
In this paper, we study the problem of minimizing the first eigenvalue of the
Laplacian plus a potential with weights, when the potential and the weight
are allowed to vary in the class of rearrangements of a given fixed potential
and weight . Our results generalized those obtained in [9] and [5].Comment: 15 page
Existence of solution to a critical equation with variable exponent
In this paper we study the existence problem for the Laplacian
operator with a nonlinear critical source. We find a local condition on the
exponents ensuring the existence of a nontrivial solution that shows that the
Pohozaev obstruction does not holds in general in the variable exponent
setting. The proof relies on the Concentration--Compactness Principle for
variable exponents and the Mountain Pass Theorem
A mass transportation approach for Sobolev inequalities in variable exponent spaces
In this paper we provide a proof of the Sobolev-Poincar\'e inequality for
variable exponent spaces by means of mass transportation methods. The
importance of this approach is that the method is exible enough to deal with
different inequalities. As an application, we also deduce the Sobolev-trace
inequality improving the result obtained by Fan.Comment: 12 page
Estimates for the Sobolev trace constant with critical exponent and applications
In this paper we find estimates for the optimal constant in the critical
Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow
\|u\|^p_{W^{1,p}(\Omega)} that are independent of . This estimates
generalized those of [3] for general . Here is the
critical exponent for the immersion and is the space dimension. Then we
apply our results first to prove existence of positive solutions to a nonlinear
elliptic problem with a nonlinear boundary condition with critical growth on
the boundary, generalizing the results of [16]. Finally, we study an optimal
design problem with critical exponent.Comment: 22 pages, submitte
The concentration-compactness principle for Orlicz spaces and applications
In this paper we extend the well-known concentration -- compactness principle
of P.L. Lions to Orlicz spaces. As an application we show an existence result
to some critical elliptic problem with nonstandard growth.Comment: 20 pages. Submitted for publicatio
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