On exponential decay of solutions of Schrödinger and Dirac equations: bounds of eigenfunctions corresponding to energies in the gaps of essential spectrum
On factorization of Fefferman's inequality
On FE-grid relocation in solving unilateral boundary value problems by FEM
We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the...
On finite difference schemes of high order accuracy for elliptic equations with mixed derivatives
On Finite Element Approximation of the Gradient for Solution of Poisson Equation.
On Finite Element Methods for the Neumann Problem.
On folding solutions of the Beltrami equation.
On Fredholm alternative for certain quasilinear boundary value problems
On Fredholm alternative for certain quasilinear boundary value problems
We study the Dirichlet boundary value problem for the -Laplacian of the form where is a bounded domain with smooth boundary , , , and is the first eigenvalue of . We study the geometry of the energy functional and show the difference between the case and the case . We also give the characterization of the right hand sides for which the above Dirichlet problem is solvable and has multiple solutions.
On fully nonlinear elliptic equations of second order
On functions, whose lines of steepest descent bend proportionally to level lines
On general boundary value problems and duality in linear elasticity. II
The present part of the paper completes the discussion in Part I in two directions. Firstly, in Section 5 a number of existence theorems for a solution to Problem III (principle of minimum potential energy) is established. Secondly, Section 6 and 7 are devoted to a discussion of both the classical and the abstract approach to the duality theory as well as the relationship between the solvability of Problem III and its dual one.
On general solvability properties of -Lapalacian-like equations
We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation where is a very general domain in , including the case .
On general two-scale convergence and its application to the characterization of -limits
We characterize some -limits using two-scale techniques and investigate a method to detect deviations from the arithmetic mean in the obtained -limit provided no periodicity assumptions are involved. We also prove some results on the properties of generalized two-scale convergence.
On generalized periodic solutions of some nonlinear telegraph and beam equations
On global existence and stationary solutions for two classes of semilinear parabolic problems
We investigate stationary solutions and asymptotic behaviour of solutions of two boundary value problems for semilinear parabolic equations. These equations involve both blow up and damping terms and they were studied by several authors. Our main goal is to fill some gaps in these studies.
On Green's Function and Eigenvalues of Nonuniformly Elliptic Boundary Value Problems.
On harmonic continuation of differentiable functions defined on a part of the boundary.
On Higher Riesz Transforms for Gaussian Measures.
On Hölder regularity for elliptic equations of non-divergence type in the plane
This paper is concerned with strong solutions of uniformly elliptic equations of non-divergence type in the plane. First, we use the notion of quasiregular gradient mappings to improve Morrey’s theorem on the Hölder continuity of gradients of solutions. Then we show that the Gilbarg-Serrin equation does not produce the optimal Hölder exponent in the considered class of equations. Finally, we propose a conjecture for the best possible exponent and prove it under an additional restriction.