Veronica Felli

Perturbation results of critical elliptic equations of Caffarelli-Kohn-Nirenberg type

Abstract We find for small e positive solutions to the equation − div (|x| −2a ∇ u)− λ |x| 2(1+a) u=(1+ek(x)) u p−1 |x| bp in R N , which branch off from the manifold of minimizers in the class of radial functions of the corresponding Caffarelli–Kohn–Nirenberg-type inequality. Moreover, our analysis highlights the symmetry-breaking phenomenon in these inequalities, namely the existence of non-radial minimizers.

Elliptic Equations with Multi-Singular Inverse-Square Potentials and Critical Nonlinearity

ABSTRACT This article deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. We show that existence of solutions heavily depends on the strength and the location of the singularities. We associate to the problem the corresponding Rayleigh quotient and give both sufficient and necessary conditions on masses and location of singularities for the minimum to be achieved. Both the cases of whole ℝ N and bounded domains are taken into account.

Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential

Asymptotics of solutions to Schroedinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis-Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order -1.

Unique Continuation Property and Local Asymptotics of Solutions to Fractional Elliptic Equations

Asymptotics of solutions to fractional elliptic equations with Hardy type potentials is studied in this paper. By using an Almgren type monotonicity formula, separation of variables, and blow-up arguments, we describe the exact behavior near the singularity of solutions to linear and semilinear fractional elliptic equations with a homogeneous singular potential related to the fractional Hardy inequality. As a consequence we obtain unique continuation properties for fractional elliptic equations.

A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type

Abstract We establish Hölder continuity of weak solutions to degenerate critical elliptic equations of Caffarelli-Kohn-Nirenberg type.

Existence of Blowing-up Solutions for a Nonlinear Elliptic Equation with Hardy Potential and Critical Growth

ABSTRACT We prove the existence of a positive solution to which blows-up at a suitable critical point of k as the positive parameter λ goes to zero.

FOUNTAIN-LIKE SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS WITH CRITICAL GROWTH AND HARDY POTENTIAL

We prove the existence of fountain-like solutions, obtained by superposition of bubbles of different blow-up orders, for a nonlinear elliptic equation with critical growth and Hardy-type potential.

Time Decay of Scaling Invariant Electromagnetic Schrödinger Equations on the Plane

We prove the sharp

Singularity of eigenfunctions at the junction of shrinking tubes, Part II

{L^1-L^\infty}