regularity for nonlinear elliptic systems of second order.
- error estimates for linear exterior problems mixed-FEM and DtN mappings
In this paper we combine the dual-mixed finite element method with a Dirichlet-to-Neumann mapping (given in terms of a boundary integral operator) to solve linear exterior transmission problems in the plane. As a model we consider a second order elliptic equation in divergence form coupled with the Laplace equation in the exterior unbounded region. We show that the resulting mixed variational formulation and an associated discrete scheme using Raviart-Thomas spaces are well posed, and derive the...
... Minimizing Currents.
3D domain decomposition method coupling conforming and nonconforming finite elements
3D domain decomposition method coupling conforming and nonconforming finite elements
This paper deals with the solution of problems involving partial differential equations in . For three dimensional case, methods are useful if they require neither domain boundary regularity nor regularity for the exact solution of the problem. A new domain decomposition method is therefore presented which uses low degree finite elements. The numerical approximation of the solution is easy, and optimal error bounds are obtained according to suitable norms.
5-Shaped Bifurcation Curves of Nonlinear Elliptic Boundary Value Problems.
𝒞1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations
We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.
(A,O)-эллиптические уравнения со слабым вырождением
"Best possible'' maximum principles
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-convergence of concentration problems
In this paper, we use -convergence techniques to study the following variational problemwhere , with , and is a bounded domain of , . We obtain a -convergence result, on which one can easily read the usual concentration phenomena arising in critical growth problems. We extend the result to a non-homogeneous version of problem . Finally, a second order expansion in -convergence permits to identify the concentration points of the maximizing sequences, also in some non-homogeneous case.
Γ-convergence of functionals on divergence-free fields
We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of Γ-convergence. We prove that the Γ-limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the Γ-limit is also stable under volume constraint and various type of boundary conditions.
-convergence of nonlinear monotone operators in perforated domains with holes of small size
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in with isolated holes of size ( a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator...
-Laplacian BVPs with linear bounded operator conditions
The aim of this paper is to present new existence results for -Laplacian boundary value problems with linear bounded operator conditions. Existence theorems are obtained using the Schauder and the Krasnosel’skii fixed point theorems. Some examples illustrate the results obtained and applications to multi-point boundary value problems are provided.
Алгеброгеометрическoе интегрирование уравнения МНШ, конечнозонные решения и их вырождения
Алгоритм блуждания по параллелепипедам для решения краевой задачи для дифференциального уравнения эллптического типа
Аналитическая формула для индекса эллиптической граничной задачи. II
Аналитическое продолжение на второй лист определителя Фредгольма резольвенты оператора Шредингера в
Аналитическое продолжение по параметру функций Грина внешних краевых задач для двумерного уравнения Гельмгольца. II
Аналитическое продолжение по параметру функций Грина внешних краевых задач для двумерного уравнения Гельмгольца. III