9 Result(s)
within
Julián Fernández Bonder
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Article
Stable Manifold Approximation for the Heat Equation with Nonlinear Boundary Condition
In this paper we study the dynamic behavior of positive solutions of the heat equation in one space dimension with a nonlinear flux boundary condition of the type u x=u p−u at x=1. We analyze the behavior of a se...
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Article
Asymptotic behavior of the eigenvalues of the one-dimensional weightedp-Laplace operator
In this paper we study the spectral counting function for the weightedp-laplacian in one dimension. First, we prove that all the eigenvalues can be obtained by a minimax characterization and then we show the exis...
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Article
Optimization of the first Steklov eigenvalue in domains with holes: a shape derivative approach
The best Sobolev trace constant is given by the first eigenvalue of a Steklov-like problem. We deal with minimizers of the Rayleigh quotient ‖u‖2 H ...
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Article
Existence results for Gradient elliptic systems with nonlinear boundary conditions
We prove the existence of nontrivial solutions to the system $$ \Delta_p u = |u|^{p-2}u,\quad \Delta_q v = |v|^{q-2}v, $$ ...
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Article
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\|_{L^{p_*}(\partial\Omega)}^p...
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Article
On the Sobolev trace Theorem for variable exponent spaces in the critical range
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 lo...
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Article
A mass transportation approach for Sobolev inequalities in variable exponent spaces
In this paper we provide a proof of the Sobolev–Poincaré inequality for variable exponent spaces by means of mass transportation methods, in the spirit of Cordero-Erausquin et al. (Adv Math 182(2):307–332, 2004)....
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Article
The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem
In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solut...
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Article
A Hölder infinity Laplacian obtained as limit of Orlicz fractional Laplacians
This paper concerns the study of the asymptotic behavior of the solutions to a family of fractional type problems on a bounded domain, satisfying homogeneous Dirichlet boundary conditions. The family of differ...
