The phase space of one generalized model by Oskolkov.
The Picard-Ionescu problem for hyperbolic inclusions with modified argument
We consider the Picard-Ionescu problem for hyperbolic inclusions with modified argument. Existence of a local solution is proved and some properties of the set of solutions are established.
The Picone identity for a class of partial differential equations
The Picone-type identity for the half-linear second order partial differential equation is established and some applications of this identity are suggested.
The point on the simple Molodensky’s problem
Il problema di Molodensky, in approssimazione sferica è detto «semplice» perchè può essere trasformato da problema di derivata obliqua a problema di Dirichlet per l’operatore di Laplace. Tale problema è accuratamente analizzato in questa Nota, con particolare riguardo alla generalizzazione delle condizioni di regolarità soddisfatte dal contorno , sufficienti a garantire l’esistenza di una soluzione fisicamente accettabile.
The point source function of the mixed difference problem in the half-plane
The Poisson equation in homogeneous Sobolev spaces.
The Poisson integral for a ball in spaces of constant curvature
We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains.
The polarization in a ferroelectric thin film: local and nonlocal limit problems
In this paper, starting from classical non-convex and nonlocal 3D-variational model of the electric polarization in a ferroelectric material, via an asymptotic process we obtain a rigorous 2D-variational model for a thin film. Depending on the initial boundary conditions, the limit problem can be either nonlocal or local.
The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation
The positive radial solutions of a class of semilinear elliptic equations.
The prescribed mean curvature equation for a revolution surface with Dirichlet condition.
The pressure equation in the fast diffusion range.
The preventive effect of the convection and of the diffusion in the blow-up phenomenon for parabolic equations
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 principal spectrum for linear nonautonomous parabolic PDEs of second order: Space-independent case
We show that the study of the principal spectrum of a linear nonautonomous parabolic PDE of second order on a bounded domain, with the Dirichlet or Neumann boundary conditions, reduces to the investigation of the spectrum of the linear nonautonomous ODE v̇ = a(t)v.
The probabilistic approach to the analysis of the limiting behavior of an integro-differential equation depending on a small parameter, and its application to stochastic processes.
The Probabilistic Solution of the Dirichlet Problem for Degenerate Elliptic Equations
We study the Dirichlet problem for degenerate elliptic equations, and show that the probabilistic solution is a unique viscosity solution.
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.