(A,O)-эллиптические уравнения со слабым вырождением
Approximation of a degenerated elliptic boundary value problem by a finite element method
Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method
The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...
Approximation of Tricomi Problem with Neumann Boundary Condition.
Asymptotic behavior of regularizable minimizers of a Ginzburg-Landau functional in higher dimensions.
Asymptotic behavior of solutions for some nonlinear partial differential equations on unbounded domains.
Asymptotic behavior of solutions to Schrödinger equations near an isolated singularity of the electromagnetic potential
Asymptotics of solutions to Schrödinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and an iterative Brezis–Kato type procedure, we describe the exact behavior near the singularity of solutions to linear and semilinear (critical and subcritical) elliptic equations with an inverse square electric potential and a singular magnetic potential with a homogeneity of order −1.
Asymptotic expansions for bounded solutions to semilinear Fuchsian equations.
Asymptotic paths for subsolutions of quasilinear elliptic equations.
Asymptotic representations for solutions of bisingular problems.
Asymptotics for the minimization of a Ginzburg-Landau energy in n dimensions
We prove that minimizers of the functional , ⊂ , n ≥ 3, which satisfy the Dirichlet boundary condition on for g: → with zero topological degree, converge in and for any α<1 - upon passing to a subsequence - to some minimizing n-harmonic map. This is a generalization of an earlier result obtained for n=2 by Bethuel, Brezis, and Hélein. An example of nonunique asymptotic behaviour (which cannot occur in two dimensions if deg g = 0) is presented.
Barriers on cones for degenerate quasilinear elliptic operators.
Beltrami equations with coefficient in the Sobolev space W1,p.
Bernstein and De Giorgi type problems: new results via a geometric approach
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
Bifurcation of nonlinear elliptic system from the first eigenvalue.
Boundary Behaviour of Nonnegative Solutions of Subelliptic Equations in NTA Domains for Carnot-Carathéodory Metrics.
Boundary value problems for some classes of degenerating second order partial differential equations.
Breaking of resonance and regularizing effect of a first order quasi-linear term in some elliptic equations
-regularity of the Aronsson equation in
convergence of minimizers of a Ginzburg-Landau functional.