o-oценки решений задачи Коши для строго гиперболического уравнения второго порядка
This paper presents two observability inequalities for the heat equation over . In the first one, the observation is from a subset of positive measure in , while in the second, the observation is from a subset of positive surface measure on . It also proves the Lebeau-Robbiano spectral inequality when is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.
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...
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
We study the realization of the operator in , where is a possibly unbounded convex open set in , is a convex unbounded function such that and , is the element with minimal norm in the subdifferential of at , and is a probability measure, infinitesimally invariant for . We show that , with domain is a dissipative self-adjoint operator in . Note that the functions in the domain of do not satisfy any particular boundary condition. Log-Sobolev and Poincaré inequalities allow...
We prove some comparison results for Monge-Ampère type equations in dimension two. We consider also the case of eigenfunctions and we prove a kind of reverse inequalities.