Traveling waves with paraboloid like interfaces for balanced bistable dynamics
Travelling fronts in cylinders
Treatment of boundary singularities in two dimensional elliptic problems by Galerkin methods
Trudinger–Moser inequality on the whole plane with the exact growth condition
Trudinger-Moser inequality is a substitute to the (forbidden) critical Sobolev embedding, namely the case where the scaling corresponds to . It is well known that the original form of the inequality with the sharp exponent (proved by Moser) fails on the whole plane, but a few modied versions are available. We prove a precised version of the latter, giving necessary and sufficient conditions for the boundedness, as well as for the compactness, in terms of the growth and decay of the nonlinear function....
Two constant sign solutions for a nonhomogeneous Neumann boundary value problem
We consider a nonlinear Neumann problem with a nonhomogeneous elliptic differential operator. With some natural conditions for its structure and some general assumptions on the growth of the reaction term we prove that the problem has two nontrivial solutions of constant sign. In the proof we use variational methods with truncation and minimization techniques.
Two Dimensional Variational Problems with Thin Obstacles.
Two Families of Mixed Finite Elements for Second Order Elliptic Problems.
Two functionals for which minimizers are also minimizers.
Two Methods of Solution of the Three-Dimensional Inverse Nodal Problem.
The operator with the Dirichlet boundary condition is considered in a parallelepiped. The problem of restoring from positions of nodal surfaces is solved.
Two notions which affected nonlinear analysis (Bernard Bolzano lecture)
General mathematical theories usually originate from the investigation of particular problems and notions which could not be handled by available tools and methods. The Fučík spectrum and the -Laplacian are typical examples in the field of nonlinear analysis. The systematic study of these notions during the last four decades led to several interesting and surprising results and revealed deep relationship between the linear and the nonlinear structures. This paper does not provide a complete survey....
Two Numerical Methods for the elliptic Monge-Ampère equation
The numerical solution of the elliptic Monge-Ampère Partial Differential Equation has been a subject of increasing interest recently [Glowinski, in 6th International Congress on Industrial and Applied Mathematics, ICIAM 07, Invited Lectures (2009) 155–192; Oliker and Prussner, Numer. Math.54 (1988) 271–293; Oberman, Discrete Contin. Dyn. Syst. Ser. B10 (2008) 221–238; Dean and Glowinski, in Partial differential equations, Comput. Methods Appl. Sci. 16 (2008) 43–63; Glowinski et al., Japan...
Two preconditioners based on the multi-level splitting of finite element spaces.
Two solutions for a nonlinear Dirichlet problem with positive forcing
Given a semilinear elliptic boundary value problem having the zero solution and where the nonlinearity crosses the first eigenvalue, we perturb it by a positive forcing term; we show the existence of two solutions under certain conditions that can be weakened in the onedimensional case.
Two symmetry problems in potential theory.
Two-dimensional curvature functionals with superquadratic growth
For two-dimensional, immersed closed surfaces , we study the curvature functionals and with integrands and , respectively. Here is the second fundamental form, is the mean curvature and we assume . Our main result asserts that critical points are smooth in both cases. We also prove a compactness theorem for -bounded sequences. In the case of this is just Langer’s theorem [16], while for we have to impose a bound for the Willmore energy strictly below as an additional condition....
Two-level additive Schwarz preconditioners for fourth-order mixed methods.
Two-scale convergence with respect to measures in continuum mechanics
Two-scale div-curl lemma
The div-curl lemma, one of the basic results of the theory of compensated compactness of Murat and Tartar, does not take over to the case in which the two factors two-scale converge in the sense of Nguetseng. A suitable modification of the differential operators however allows for this extension. The argument follows the lines of a well-known paper of F. Murat of 1978, and uses a two-scale extension of the Fourier transform. This result is also extended to time-dependent functions, and is applied...
Two-sided a posteriori error estimates for linear elliptic problems with mixed boundary conditions
The paper is devoted to verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model consisting of a linear elliptic (reaction-diffusion) equation with a mixed Dirichlet/Neumann/Robin boundary condition is considered...
Two-sided bounds of eigenvalues of second- and fourth-order elliptic operators
This article presents an idea in the finite element methods (FEMs) for obtaining two-sided bounds of exact eigenvalues. This approach is based on the combination of nonconforming methods giving lower bounds of the eigenvalues and a postprocessing technique using conforming finite elements. Our results hold for the second and fourth-order problems defined on two-dimensional domains. First, we list analytic and experimental results concerning triangular and rectangular nonconforming elements which...