Convergence of the Nonconforming Wilson Element for Arbitrary Quadrilateral Meshes.
Convergence of -cycle and -cycle multigrid methods for the biharmonic problem using the Morley element.
Convergence rate estimate for a domain decomposition method.
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem
In this paper, a class of cell centered finite volume schemes, on general unstructured meshes, for a linear convection-diffusion problem, is studied. The convection and the diffusion are respectively approximated by means of an upwind scheme and the so called diamond cell method [4]. Our main result is an error estimate of order h, assuming only the W2,p (for p>2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in...
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes...
Convergence to a positive equilibrium for some nonlinear evolution equations in a ball.
Convergent algorithms suitable for the solution of the semiconductor device equations
In this paper, two algorithms are proposed to solve systems of algebraic equations generated by a discretization procedure of the weak formulation of boundary value problems for systems of nonlinear elliptic equations. The first algorithm, Newton-CG-MG, is suitable for systems with gradient mappings, while the second, Newton-CE-MG, can be applied to more general systems. Convergence theorems are proved and application to the semiconductor device modelling is described.
Converse problem for the two-component radial Gross-Pitaevskii system with a large coupling parameter
We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a segregated limiting profile, with the difference of its components satisfying a limit scalar PDE. In the case of radial symmetry, under natural non-degeneracy assumptions on a solution of the limit problem, we establish by a perturbation argument its persistence...
Convessità della goccia appoggiata
Convex functions on Carnot groups.
Convex integration with constraints and applications to phase transitions and partial differential equations
We study solutions of first order partial differential relations , where is a Lipschitz map and is a bounded set in matrices, and extend Gromov’s theory of convex integration in two ways. First, we allow for additional constraints on the minors of and second we replace Gromov’s −convex hull by the (functional) rank-one convex hull. The latter can be much larger than the former and this has important consequences for the existence of ‘wild’ solutions to elliptic systems. Our work was originally...
Convex shape optimization for the least biharmonic Steklov eigenvalue
The least Steklov eigenvalue d1 for the biharmonic operator in bounded domains gives a bound for the positivity preserving property for the hinged plate problem, appears as a norm of a suitable trace operator, and gives the optimal constant to estimate the L2-norm of harmonic functions. These applications suggest to address the problem of minimizing d1 in suitable classes of domains. We survey the existing results and conjectures about this topic; in particular, the existence of a convex domain...
Convex symmetrization and applications
Convexity estimates for nonlinear elliptic equations and application to free boundary problems
Convexity of level sets for solutions to nonlinear elliptic problems in convex rings.
Corner Mellin operators and conormal asymptotics
Correction "Almost everywhere summability of eiegnfunction expansion associated to elliptic operators" by Waldemar Hebish, Studia Math. 96(3) 1990, 263-275
Correction to my paper: “Existence theorems for operator equations and nonlinear elliptic boundary-value problems” [Comment. Math. Univ. Carolinae 14 (1973), 27-46]