arXiv subjects

J. Fernández Bonder

Publications and source records attributed to J. Fernández Bonder.

3 recordsLinked to original sources

arXiv2023

A priori estimates for solutions of $g$-Laplace type problems

In this work we study a priori bounds for weak solution to elliptic problems with nonstandard growth that involves the so-called $g-$Laplace operator. The $g-$Laplacian is a generalization of the $p-$Laplace operator that takes into account different behaviors than pure powers. The method to obtain this a priori estimates is the so called ``blow-up'' argument developed by Gidas and Spruck. Then we applied this a priori bounds to show some existence results for these problems.

math.AP↗

arXiv2015

Eigenvalue homogenization problem with indefinite weights

In this work we study the homogenization problem for nonlinear elliptic equations involving $p-$Laplacian type operators with sign changing weights. We study the asymptotic behavior of variational eigenvalues, which consist on a double sequence of eigenvalues. We show that the $k-$th positive eigenvalue goes to infinity when the average of the weight is nonpositive, and converge to the $k-$th variational eigenvalue of the limit problem when the average is positive for any $k\ge 1$.

math.AP↗

arXiv2015

A Lyapunov type Inequality for Indefinite Weights and Eigenvalue Homogenization

In this paper we prove a Lyapunov type inequality for quasilinear problems with indefinite weights. We show that the first eigenvalue is bounded below in terms of the integral of the weight, instead of the integral of its positive part. We apply this inequality to some eigenvalue homogenization problems with indefinite weights.

math.AP↗