Estimates for the Green function and existence of positive solutions for higher-order elliptic equations.
Estimates for the multiplicative square function of solutions to nondivergence elliptic equations.
Estimates for the -Neumann operator on strongly pseudo-convex domain with Lipschitz boundary.
Estimates in Besov spaces for transport and transport-diffusion equations with almost Lipschitz coefficients.
This paper aims at giving an overview of estimates in general Besov spaces for the Cauchy problem on t = 0 related to the vector field ∂t + v·∇. The emphasis is on the conservation or loss of regularity for the initial data.When ∇u belongs to L1(0,T; L∞) (plus some convenient conditions depending on the functional space considered for the data), the initial regularity is preserved. On the other hand, if ∇v is slightly less regular (e.g. ∇v belogs to some limit space for which the embedding in L∞...
Estimates near the boundary for solutions of second order parabolic equations.
Estimates of solutions of impulsive parabolic equations and applications to the population dynamics.
A theorem on estimates of solutions of impulsive parabolic equations by means of solutions of impulsive ordinary differential equations is proved. An application to the population dynamics is given.
Estimates of solutions to linear elliptic systems and equations
Whenever nonlinear problems have to be solved through approximation methods by solving related linear problems a priori estimates are very useful. In the following this kind of estimates are presented for a variety of equations related to generalized first order Beltrami systems in the plane and for second order elliptic equations in . Different types of boundary value problems are considered. For Beltrami systems these are the Riemann-Hilbert, the Riemann and the Poincaré problem, while for elliptic...
Estimates of the derivatives for a class of parabolic degenerate operators with unbounded coefficients in
We consider a class of perturbations of the degenerate Ornstein-Uhlenbeck operator in . Using a revised version of Bernstein’s method we provide several uniform estimates for the semigroup associated with the realization of the operator in the space of all the bounded and continuous functions in
Estimates of weak solutions to nondiagonal quasilinear parabolic systems
-estimates of weak solutions are established for a quasilinear non-diagonal parabolic system with a special structure whose leading terms are modelled by p-Laplacians. A generalization of the weak maximum principle to systems of equations is employed.
Estimates of weighted Hölder norms of the solutions to a parabolic boundary value problem in an initially degenerate domain
A-priori estimates in weighted Hölder norms are obtained for the solutions of a one- dimensional boundary value problem for the heat equation in a domain degenerating at time t = 0 and with boundary data involving simultaneously the first order time derivative and the spatial gradient.
Estimates on the solution of an elliptic equation related to Brownian motion with drift.
In this paper we are concerned with studying the Dirichlet problem for an elliptic equation on a domain in R3. For simplicity we shall assume that the domain is a ball ΩR of radius R. Thus:ΩR = {x ∈ R3 : |x| < R}.The equation we are concerned with is given by(-Δ - b(x).∇) u(x) = f(x), x ∈ ΩR,with zero Dirichlet boundary conditions.
Estimation à priori des solutions faibles de certains systèmes non linéaires elliptiques
Estimations de Schauder et régularité höldérienne pour une classe de problèmes aux limites elliptiques singuliers
Estimations de Strichartz généralisées sur le groupe de Heisenberg
Estimations hölderiennes pour l'équation d'Euler
Estimations limites pour la solution canonique de l'équation ...u = f.
Estimations pour dans des domaines non pseudo-convexes
Nous étudions les domaines de qui satisfont (localement) à l’estimation suivante :où est un voisinage d’un point du bord .L’intérêt de cette estimation réside dans son utilisation pour montrer une estimation sous-elliptique. Remarquons qu’elle est toujours satisfaite par les domaines pseudo-convexes, ce qui rend naturel le fait qu’elle soit liée au comportement dans des parties négatives des valeurs propres de la forme de Levi.
Estimées de Strichartz pour l’équation de Schrödinger à coefficients variables
Évolution d'une interface par capillarité et diffusion de volume. Estimations a priori et résultats d'existence
Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.