- theory for a class of singular elliptic differential operators, II
spaces and their application to elliptic partial differential operators
-оценки решения смешанной задачи с условиями Дирихле для волнового уравнения при радиальных начальных данных
estimates for damped wave equations with odd initial data.
L1 and L∞-estimates with a local weight for the ∂-equation on convex domains in Cn.
We construct a defining function for a convex domain in Cn that we use to prove that the solution-operator of Henkin-Romanov for the ∂-equation is bounded in L1 and L∞-norms with a weight that reflects not only how near the point is to the boundary of the domain but also how convex the domain is near the point. We refine and localize the weights that Polking uses in [Po] for the same type of domains because they depend only on the Euclidean distance to the boudary and don't take into account the...
La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente. (I) Deduzione di limitazioni a priori sulla temperatura e le sue derivate
Large time regular solutions to the MHD equations in cylindrical domains
We prove the large time existence of solutions to the magnetohydrodynamics equations with slip boundary conditions in a cylindrical domain. Assuming smallness of the L₂-norms of the derivatives of the initial velocity and of the magnetic field with respect to the variable along the axis of the cylinder, we are able to obtain an estimate for the velocity and the magnetic field in without restriction on their magnitude. Then the existence follows from the Leray-Schauder fixed point theorem.
Lateral estimates for iterated elliptic operators and analyticity.
Le problème de Cauchy à caractéristiques multiples
Le problème de Cauchy dans des espaces locaux pour l'équation de Ginzburg-Landau complexe
Le problème mixte des équations des ondes et applications
Le problème mixte hyperbolique
Line Method Approximations to the Cauchy Problem for Nonlinear Parabolic Differential Equations.
Linear elliptic operators with measurable coefficients
Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions
We study one-dimensional linear hyperbolic systems with -coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.
Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.
Liouville theorems and blow up behaviour in semilinear reaction diffusion systems
Liouville theorems for a class of linear second-order operators with nonnegative characteristic form.
Liouville Theorems for Nonlinear Elliptic Equations and Systems.
Liouville-type theorems and asymptotic behavior of nodal radial solutions of semilinear heat equations
We prove a Liouville type theorem for sign-changing radial solutions of a subcritical semilinear heat equation . We use this theorem to derive a priori bounds, decay estimates, and initial and final blow-up rates for radial solutions of rather general semilinear parabolic equations whose nonlinearities have a subcritical polynomial growth. Further consequences on the existence of steady states and time-periodic solutions are also shown.