Some elliptic problems with singular natural growth lower order terms

Renormalized Solutions for Strongly Nonlinear Elliptic Problems with Lower Order Terms and Measure Data in Orlicz-Sobolev Spaces

The purpose of this paper is to prove the existence of a renormalized solution of perturbed elliptic problems$ -operatorname{div}Big(a(x,u,nabla u)+Phi(u) Big)+ g(x,u,nabla u) = mumbox{ in }Omega,  $ in the framework of Orlicz-Sobolev spaces without any restriction on the $M$ N-function of the Orlicz spaces, where $-operatorname{div}Big(a(x,u,nabla u)Big)$ is a Leray-Lions operator defined f...

Two weak solutions for some singular fourth order elliptic problems

In this paper, we establish the existence of at least two distinct weak solutions for some singular elliptic problems involving a p-biharmonic operator, subject to Navier boundary conditions in a smooth bounded domain in RN . A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least two distinct nontrivial weak solutions.

Boundary value problems for elliptic operators with singular drift terms

Let Ω be a Lipschitz domain in R, n ≥ 3, and L = divA∇ − B∇ be a second order elliptic operator in divergence form with real coefficients such that A is a bounded elliptic matrix and the vector field B ∈ Lloc(Ω) is divergence free and satisfies the growth condition dist(X, ∂Ω)|B(X)| ≤ ε1 for ε1 small in a neighbourhood of ∂Ω. For these elliptic operators we will study on the basis of the theory...

Dirichlet Problems with Singular Convection Terms and Applications to Some Elliptic Systems

To be more precise, in [2] is proved the existence of u { weak solution belonging to W 1,2 0 (Ω) ∩ L ∗∗ (Ω), if m ≥ 2N N+2 (“Stampacchia” theory); distributional solution belonging to W 1,m ∗ 0 (Ω), if 1 < m < 2N N+2 (“Calderon-Zygmund” theory); (5) where m∗ = mN N−m (1 ≤ m < N) and m ∗∗ = mN N−2m (1 ≤ m < N 2 ). Note that the above existence results are exactly the results proved with E = 0 in...

Title AN L^p-APPROACH TO SINGULAR LINEAR PARABOLIC EQUATIONS WITH LOWER ORDER TERMS