Infinitely many radial solutions of an elliptic system
-approximation of generalized biaxially symmetric potentials over Carathéodory domains
La conjecture de Kato
L'equazione . Teoremi di completezza
In ipotesi molto generali si dimostrano teoremi di completezza nel senso di Picone per l'equazione (1). Come corollario si ottengono teoremi del tipo Runge.
L'equazione . Calcolo dell'indice dei problemi al contorno e soluzioni deboli
It is proved that Lopatinskii's condition is necessary and sufficient for problem (2.5) to be an index problem. A method is given for the determination of the index.
Limit behaviour of singular solutions of some semilinear elliptic equations
Linear elliptic operators with measurable coefficients
Liouville theorems for a class of linear second-order operators with nonnegative characteristic form.
Local energy decay for several evolution equations on asymptotically euclidean manifolds
Let be a long range metric perturbation of the Euclidean Laplacian on , . We prove local energy decay for the solutions of the wave, Klein-Gordon and Schrödinger equations associated to . The problem is decomposed in a low and high frequency analysis. For the high energy part, we assume a non trapping condition. For low (resp. high) frequencies we obtain a general result about the local energy decay for the group where has a suitable development at zero (resp. infinity).
Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation We then give conditions for the convergence, as , of the solution of the evolution equation to its stationary state.
Lp bounds for Riesz transforms and square roots associated to second order elliptic operators.
Maximum Principles for Linear, Non-Unifomly Elliptic Operators with Measurable Coefficients.
Maximum principles for some quasilinear second order partial differential equations
Milton's conjecture on the regularity of solutions to isotropic equations
Moltiplicatori spettrali per l'operatore di Ornstein-Uhlenbeck
Questa è una rassegna di alcuni risultati recenti sui moltiplicatori spettrali dell'operatore di Ornstein-Uhlenbeck, un laplaciano naturale sullo spazio euclideo munito della misura gaussiana. I risultati sono inquadrati nell'ambito della teoria generale dei moltiplicatori spettrali per laplaciani generalizzati.
Nonexistence of Coherent Structures in Two-dimensional Inviscid Channel Flow
Two-dimensional inviscid channel flow of an incompressible fluid is considered. It is shown that if the flow is steady and features no horizontal stagnation, then the flow must necessarily be a parallel shear flow.
Nonlocal Robin problem for elliptic second order equations in a plane domain with a boundary corner point
We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
Nonunique continuation for plane uniformly elliptic equations in Sobolev spaces
Numerical treatment of 3-dimensional potential problem
Assuming an incident wave to be a field source, we calculate the field potential in a neighborhood of an inhomogeneous body. This problem which has been formulated in can be reduced to a bounded domain. Namely, a boundary condition for the potential is formulated on a sphere. Then the potential satisfies a well posed boundary value problem in a ball containing the body. A numerical approximation is suggested and its convergence is analyzed.
Observations on estimates for divergence elliptic equations with VMO coefficients
In this paper, we make some observations on the work of Di Fazio concerning estimates, , for solutions of elliptic equations , on a domain with Dirichlet data whenever and . We weaken the assumptions allowing real and complex non-symmetric operators and boundary. We also consider the corresponding inhomogeneous Neumann problem for which we prove the similar result. The main tool is an appropriate representation for the Green (and Neumann) function on the upper half space. We propose...