Sergio Segura de León

Bounded and unbounded solutions for a class of quasi-linear elliptic problems with a quadratic gradient term

Abstract Our aim in this article is to study the following nonlinear elliptic Dirichlet problem: − div [a(x,u)·∇u]+b(x,u,∇u)=f, in Ω; u=0, on ∂Ω; where Ω is a bounded open subset of RN, with N>2, f∈L m (Ω) . Under wide conditions on functions a and b, we prove that there exists a type of solution for this problem; this is a bounded weak solution for m>N/2, and an unbounded entropy solution for N/2>m⩾2N/(N+2). Moreover, we show when this entropy solution is a weak one and when can be taken as test function in the weak formulation. We also study the summability of the solutions.

REGULARITY FOR ENTROPY SOLUTIONS OF PARABOLIC p-LAPLACIAN TYPE EQUATIONS

In this note we give some summability results for entropy solutions of the nonlinear parabolic equation

The Dirichlet problem for a singular elliptic equationarising in the level set formulation of the inverse mean curvatureflow

u_t -\operatorname{div} {\mathbf a}_p (x,\nabla u) = f

Bounded solutions to the 1-Laplacian equation with a critical gradient term

in

On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising

]0,T[\times \Omega

Quasilinear stationary problems with a quadratic gradient term having singularities

with initial datum in

Global Existence for Nonlinear Parabolic Problems With Measure Data– Applications to Non-uniqueness for Parabolic Problems With Critical Gradient terms

L^1(\Omega)

Elliptic problems involving the 1-Laplacian and a singular lower order term: THE 1-LAPLACIAN EQUATION WITH A SINGULAR LOWER ORDER TERM

and assuming Dirichlets boundary condition, where

Regularity of Renormalized Solutions to Nonlinear Elliptic Equations Away from the Support of Measure Data

{\mathbf a}_p(.,.)

Multiplicity of Solutions to Elliptic Problems Involving the 1-Laplacian with a Critical Gradient Term

is a Caratheodory function satisfying the classical Leray-Lions hypotheses,