Maria Michaela Porzio

L∞-solutions for some nonlinear degenerate elliptic and parabolic equations

AbstractIn this paper we prove the existence of bounded solutions for equations whose prototype is:

Existence results for quasilinear elliptic and parabolic problems with quadratic gradient terms and sources

- div\left( {v\left( x \right)\left| {Du} \right|^{p - 2} Du} \right) + v_0 \left( x \right)u\left| u \right|^{p - 2} = v\left( x \right)\left| {Du} \right|^p + f\left( x \right) - div\left( {g\left( x \right)} \right)

On decay estimates

in a bounded open set Ω, u=0 on ∂Ω. We also consider the evolution case.

Elliptic Equations with Degenerate Coercivity: Gradient Regularity

In this paper we prove an existence result for a class of quasi-linear parabolic problems whose prototype is the following

Parabolic equations with non–linear, degenerate and space–time dependent operators

\left\{ {\begin{array}{*{20}{c}} {{u_{t}} - div\left[ {a\left( u \right)\nabla u} \right] = \beta \left( u \right){{\left| {\nabla u} \right|}^{2}} + f\left( {x,t} \right){\text{ in }}{\Omega _{{T,}}}} \\ {u\left( {x,t} \right) = 0{\text{ in }}\partial \Omega x\left( {0,T} \right),} \\ {u\left( {x,0} \right) = {u_{0}}{\text{ in }}\Omega .} \\ \end{array} } \right.

Existence, uniqueness and behavior of solutions for a class of nonlinear parabolic problems

(1)