Daniela Giachetti

Results on Parabolic Equations Related to Some Caffarelli--Kohn--Nirenberg Inequalities

In this paper problem \begin{equation}\label{lamadrenaturaleza} \left\{\!\!\! \begin{array}{ll} u_t-\Div(|x|^{-p\gamma}|\nabla u|^{p-2}\nabla u) =\lambda\dfrac{u^{p-2}u}{|x|^{p(\gamma+1)}} \quad\hbox{in } \Omega\times(0,\infty),\ 0\in\Omega,\\ u(x,t)=0 \quad\hbox{on } \partial\Omega\times(0,\infty),\\[2pt] u(x,0)=\psi(x)\geq 0 \end{array} \right. \end{equation} is studied when

On the regularity of very weak minima

1 < p< N

Existence results via regularity for some nonlinear elliptic problems

,

Strongly nonlinear unilateral problems

-\infty < (\gamma+1) < \frac{N}{p}

Existence and Homogenization for a Singular Problem Through Rough Surfaces

, and under hypotheses on the initial data.

Advances in the Study of Singular Semilinear Elliptic Problems

We consider very weak minimisers u of variational integrals ∫ F(x, Du(x)) dx and very weak solutions u of nonlinear elliptic systems div A ( x, u, Du ) = 0; we prove higher integrability for the gradient Du without any homogeneity on ξ→A ( x,u,ξ ) thus improving on a result by Iwaniec and Sbordone.

Minima of some non convex non coercive problems

This paper is concerned with existence and regularity of the problem where Ω is a bounded open set of , A is a Leray—Lions operator on and g is a nonlinear lower order term having growth of order p with respect to (we do not assume any growth restriction with respect to ) and such that

A generalization of a theorem of H. Brezis & F. E. Browder and applications to some unilateral problems

This paper will be concerned with the existence of the solutions to the strongly nonlinear unilateral (and bilateral) problems. Furthermore, some other properties of the solutions are proved.

Quasilinear stationary problems with a quadratic gradient term having singularities

The paper deals with existence and homogenization for elliptic problems with lower order terms singular in the u-variable (u is the solution) in a cylinder

Stability results for two classes of nonlinear unilateral problems

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