-estimates near the boundary for solutions of the Dirichlet problem
-inequalities for the laplacian and unique continuation
We prove an inequality of the typeThis is then used to derive the unique continuation property for the differential inequality under suitable local integrability assumptions on the function .
--Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
We prove the --time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the --time decay estimates.
time decay estimates for the solution of the linear partial differential equations of thermodiffusion
We consider the initial-value problem for a linear hyperbolic parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove time decay estimates for the solution of the associated linear Cauchy problem.
-oценки решений задачи Коши для одномерного гиперболического уравнения
-oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами
regularity for weak solutions of parabolic systems
-regularity of solutions to first initial-boundary value problem for hyperbolic equations in cusp domains.
regularity of velocity averages
-resolvent estimates and time decay for generalized thermoelastic plate equations.
-spectrum of Ornstein-Uhlenbeck operators
- theory for a class of singular elliptic differential operators, II
-theory for a class of singular elliptic differential operators
-theory of boundary value problems for Sobolev type equations
-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle.
-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle
-uniqueness for infinite dimensional symmetric Kolmogorov operators : the case of variable diffusion coefficients
spaces and their application to elliptic partial differential operators
-оценки решения смешанной задачи с условиями Дирихле для волнового уравнения при радиальных начальных данных
-approach to weak solutions of the Oseen flow around a rotating body
We consider the time-periodic Oseen flow around a rotating body in ℝ³. We prove a priori estimates in -spaces of weak solutions for the whole space problem under the assumption that the right-hand side has the divergence form. After a time-dependent change of coordinates the problem is reduced to a stationary Oseen equation with the additional term -(ω ∧ x)·∇u + ω ∧ u in the equation of momentum where ω denotes the angular velocity. We prove the existence of generalized weak solutions in -space...