A sign-changing solution for a superlinear Dirichlet problem. II.
A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain Ω ⊂ ℝ2the functional is I ϵ ( u ) = 1 2 ∫ Ω ϵ -1 1 − Du 2 2 + ϵ D 2 u 2 d z whereubelongs to the subset of functions in W02,2(Ω) whose gradient (in the sense of trace) satisfiesDu(x)·ηx = 1 where ηx is the inward pointing unit normal to ∂Ω at x. In [Ann. Sc. Norm. Super. Pisa Cl....
A simple proof of the characterization of functions of low Aviles Giga energy on a ball via regularity
The Aviles Giga functional is a well known second order functional that forms a model for blistering and in a certain regime liquid crystals, a related functional models thin magnetized films. Given Lipschitz domain Ω ⊂ ℝ2 the functional is where u belongs to the subset of functions in whose gradient (in the sense of trace) satisfies Du(x)·ηx = 1 where ηx is the inward pointing unit normal ...
A singular equation with positive and free boundary solutions.
Para 0 < β < 1 consideramos la ecuación -Δu = χ{u > 0} (-u-β + λf(x, u)) en Ω con condición de borde tipo Dirichlet. Esta ecuación posee una solución maximal uλ ≥ 0 para todo λ > 0. Si λ es menor que una cierta constante λ*, uλ se anula en el interior del dominio creando una frontera libre, y para λ > λ* esta solución es positiva en Ω y estable. Establecemos la regularidad de uλ incluso en presencia de una frontera libre. Para λ ≥ λ* la solución del problema...
A singular Gierer—Meinhardt system of elliptic equations
A singular ODE related to quasilinear elliptic equations.
A Singular Solution of the Capillary Equation. I. Existence.
A Singular Solution of the Capillary Equation. II. Uniqueness.
A solid-fluid model with unilateral contact conditions.
A solution method of the Signorini problem.
A special finite element method based on component mode synthesis
The goal of our paper is to introduce basis functions for the finite element discretization of a second order linear elliptic operator with rough or highly oscillating coefficients. The proposed basis functions are inspired by the classic idea of component mode synthesis and exploit an orthogonal decomposition of the trial subspace to minimize the energy. Numerical experiments illustrate the effectiveness of the proposed basis functions.
A spherical Harnack inequality for singular solutions of nonlinear elliptic equations
A splitting formula for an electromagnetic diffraction problem.
A stability result for -harmonic systems with discontinuous coefficients.
A stable mixed finite element method on truncated exterior domains
A stable multigrid strategy for convection-diffusion using high order compact discretization.
A Static condensation Reduced Basis Element method : approximation and a posteriori error estimation
We propose a new reduced basis element-cum-component mode synthesis approach for parametrized elliptic coercive partial differential equations. In the Offline stage we construct a Library of interoperable parametrized reference components relevant to some family of problems; in the Online stage we instantiate and connect reference components (at ports) to rapidly form and query parametric systems. The method is based on static condensation at the interdomain level, a conforming eigenfunction “port”...
A Stationary Schrödinger-Poisson System Arising from the Modelling of Electronic Devices.
A stationary Stefan problem with convection and nonlinear diffusion.
A stochastic impulse control problem with quadratic growth Hamiltonian and the corresponding quasi variational inequality.