The Non-Existence of Branch Points in Solutions to Certain Classes of Plateau Type Variational Problems.
The nonlinear Neumann problem and sharp weighted Sobolev inequalities
We prove sharp inequalities in weighted Sobolev spaces. Our approach is based on the blow-up technique applied to some nonlinear Neumann problems.
The obstacle problem for the -harmonic equation.
The oscillatory behavior of second order nonlinear elliptic equations.
The -Laplace eigenvalue problem as in a Finsler metric
We consider the -Laplacian operator on a domain equipped with a Finsler metric. We recall relevant properties of its first eigenfunction for finite and investigate the limit problem as .
The -Laplacian and connected pairs of functions.
The PDE describing constant mean curvature surfaces
We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.
The p-harmonic system with measure-valued right hand side
The principal eigenvalue of the ∞-laplacian with the Neumann boundary condition
We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
The principal eigenvalue of the ∞-Laplacian with the Neumann boundary condition
We prove the existence of a principal eigenvalue associated to the ∞-Laplacian plus lower order terms and the Neumann boundary condition in a bounded smooth domain. As an application we get uniqueness and existence results for the Neumann problem and a decay estimate for viscosity solutions of the Neumann evolution problem.
The reverse Hölder inequality for the solution to -harmonic type system.
The speed of propagation for KPP type problems. I: Periodic framework
This paper is devoted to some nonlinear propagation phenomena in periodic and more general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...
The summability of solutions to variational problems since Guido Stampacchia.
Inequalities concerning the integral of |∇u|2 on the subsets where |u(x)| is greater than k can be used in order to prove regularity properties of the function u. This method was introduced by Ennio De Giorgi e Guido Stampacchia for the study of the regularity of the solutions of Dirichlet problems.
The topological asymptotic for the Navier-Stokes equations
The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional...
The topological asymptotic for the Navier-Stokes equations
The aim of the topological asymptotic analysis is to provide an asymptotic expansion of a shape functional with respect to the size of a small inclusion inserted inside the domain. The main field of application is shape optimization. This paper addresses the case of the steady-state Navier-Stokes equations for an incompressible fluid and a no-slip condition prescribed on the boundary of an arbitrary shaped obstacle. The two and three dimensional cases are treated for several examples of cost functional...
The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
The Wiener criterion and quasilinear uniformly elliptic equations
Theorems of existence and multiplicity for nonlinear elliptic problems with noninvertible linear part
Thermistor problem: a nonlocal parabolic problem.
Three nodal solutions of singularly perturbed elliptic equations on domains without topology