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On W1,p estimates for elliptic equations in divergence form

- L. Caffarelli, I. Peral
- Mathematics
- 1998

First, we will apply the method to study W 1,p regularity for a nonlinear elliptic operator in divergence form. We would like to point out that in the particular case of a linear elliptic equation,… Expand

Multiplicity Results for Some Nonlinear Elliptic Equations

- A. Ambrosetti, J. G. Azorero, I. Peral
- Mathematics
- 10 April 1996

Abstract This paper deals with the existence of multiple solutions for some classes of nonlinear elliptic Dirichlet boundary value problems. The interplay of convex and concave nonlinearities is… Expand

A convex-concave problem with a nonlinear boundary condition

- J. García-Azorero, I. Peral, J. Rossi
- Mathematics
- 20 March 2004

Perturbation of Δu+u(N+2)/(N−2)=0, the Scalar Curvature Problem in RN, and Related Topics

- A. Ambrosetti, J. G. Azorero, I. Peral
- Mathematics
- 20 June 1999

Abstract Some nonlinear elliptic equations on R N which arise perturbing the problem with the critical Sobolev exponent are studied. In particular, some results dealing with the scalar curvature… Expand

Existence and nonexistence results for quasilinear elliptic equations involving the p-laplacian

- B. Abdellaoui, V. Felli, I. Peral
- Mathematics
- 2006

The paper deals with the study of a quasilinear elliptic equation involving the p-laplacian with a Hardy-type singular potential and a critical nonlinearity. Existence and nonexistence results are… Expand

Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential

- S. Dipierro, L. Montoro, I. Peral, B. Sciunzi
- Mathematics
- 24 June 2015

We prove existence, qualitative properties and asymptotic behavior of positive solutions to the doubly critical problem $$\begin{aligned} (-\Delta )^s u=\vartheta \frac{u}{|x|^{2s}}+u^{2_s^*-1},… Expand

Some results for semilinear elliptic equations with critical potential

- B. Abdellaoui, I. Peral
- MathematicsProceedings of the Royal Society of Edinburgh…
- 1 February 2002

This paper is devoted to the study of the elliptic problems with a critical potential, where N ≥ 3, λ ≥ 0 and 0 < q < 1 < p ≤ (N + 2)/(N − 2). Existence, multiplicity, behaviour in x = 0 and… Expand

Some remarks on the solvability of non-local elliptic problems with the Hardy potential

- B. Barrios, M. Medina, I. Peral
- Mathematics
- 14 July 2014

The aim of this paper is to study the solvability of the following problem, where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded… Expand

Some improved Caffarelli-Kohn-Nirenberg inequalities

- B. Abdellaoui, E. Colorado, I. Peral
- Mathematics
- 1 July 2005

Abstract.For 1 < p < N and $-\infty < \gamma < \frac{N-p}{p}$ we obtain the following improved Hardy-Sobolev Inequalities$$ \int\limits_\Omega \vert\nabla \phi\vert^p\vert x\vert^{-p\gamma}dx… Expand

Existence and nonexistence results for quasilinear elliptic equations involving the p-Laplacian with a critical potential

- B. Abdellaoui, I. Peral
- Mathematics
- 14 March 2003

This paper deals with the existence and nonexistence results for quasilinear elliptic equations of the form -Δpu=f(x, u), where Δp:=div(|∇u|p-2∇u), p>1, and the solutions are understood in the sense… Expand

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