相关论文: Optimal three-ball inequalities and quantitative u…
In this paper we obtain new well-possedness results concerning a linear inhomogenous Stokes-like system. These results are used to establish local well-posedness in the critical spaces for initial density $\rho_{0}$ and velocity $u_{0}$…
We consider the Stokes eigenvalue problem in open balls and open annuli in R3 with homogeneous Dirichlet boundary conditions. Using the frame of toroidal and poloidal fields we construct the othogonal decomposition of the Stokes eigenvalue…
This paper is devoted to the well-posedness analysis of a nonstationary Stokes hemivariational inequality for an incompressible fluid flow described by the Stokes equations subject to a nonsmooth boundary condition of friction type…
In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients, we are interested in a Carleman-type inequality for these solutions satisfying an additional growth condition in elliptic…
In this paper we derive local estimates of solutions of the Perturbed Stokes system. This system arises as a reduction of the Stokes system near a curved part of the boundary of the domain if one applies a diffeomorphism flatting the…
We establish near-optimal quantitative uniqueness of continuation for solutions of evolution equations vanishing on the lateral boundary. These results were obtained simply by combining existing observability inequalities and energy…
The aim of this note is to present a numerical method to solve the Stokes problem in a bounded domain with a Dirac source term, which preserves optimality for any approximation order by the finite-element method. It is based on the…
We study the Stokes phenomenon via hyperfunctions for the solutions of the 1-dimensional complex heat equation under the condition that the Cauchy data are holomorphic on $\mathbb{C}$ but a finitely many singular or branching points with…
We study the regularity and finite element approximation of the axisymmetric Stokes problem on a polygonal domain $\Omega$. In particular, taking into account the singular coefficients in the equation and non-smoothness of the domain, we…
We give a sharp upper bound on the vanishing order of solutions to Schrodinger equation with C^1 electric and magnetic potentials on a compact smooth manifold. Our method is based on quantitative Carleman type inequalities developed by…
A class of quasi-variational-hemivariational inequalities in reflexive Banach spaces is studied. The inequalities contain a convex potential, a locally Lipschitz superpotential, and an implicit obstacle set of constraints. Results on the…
The velocity solution of the incompressible Stokes equations is not affected by changes of the right hand side data in form of gradient fields. Most mixed methods do not replicate this property in the discrete formulation due to a…
In this paper, we analyze the convergence and optimality of a standard adaptive nonconforming linear element method for the Stokes problem. After establishing a special quasi--orthogonality property for both the velocity and the pressure in…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
In this paper we consider the Navier-Stokes Equations in 3 dimensions in the vorticity formulation in the absence of the external forces. We derive upper bounds on L_{infinity} norm of omega and use them together with the Local Existence…
This paper is devoted to a study of the unique continuation property for stochastic parabolic equations. Due to the adapted nature of solutions in the stochastic situation, classical approaches to treat the the unique continuation problem…
We propose stochastic optimization algorithms that can find local minima faster than existing algorithms for nonconvex optimization problems, by exploiting the third-order smoothness to escape non-degenerate saddle points more efficiently.…
We establish a strong unique continuation property for stochastic parabolic equations. Our method is based on a suitable stochastic version of Carleman estimate. As far as we know, this is the first result for strong unique continuation…
In this article we present a new strategy of addressing the (variable coefficient) thin obstacle problem. Our approach is based on a (variable coefficient) Carleman estimate. This yields semi-continuity of the vanishing order, lower and…
We establish the validity of a strong unique continuation property for weakly coupled elliptic systems, including competitive ones. Our proof exploits the system structure and uses Carleman estimates. We apply this result to obtain some…