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On the fusion problem for degenerate elliptic equations II

Stephen M. Buckley, Pekka Koskela (1999)

Commentationes Mathematicae Universitatis Carolinae

Let F be a relatively closed subset of a Euclidean domain Ω . We investigate when solutions u to certain elliptic equations on Ω F are restrictions of solutions on all of Ω . Specifically, we show that if F is not too large, and u has a suitable decay rate near F , then u can be so extended.

On the G -convergence of Morrey operators

Maria Rosaria Formica, Carlo Sbordone (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Following Morrey [14] we associate to any measurable symmetric 2 × 2 matrix valued function A x such that ξ 2 K A x ξ , ξ K ξ 2 a.e. x Ω , ξ R 2 , Ω R 2 ...

On the homogenization of the Poisson equation in partially perforated domains with arbitrary density of cavities and mixed type conditions on their boundary

Olga A. Oleinik, Tatiana A. Shaposhnikova (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In this paper we study the behavior of solutions of the boundary value problem for the Poisson equation in a partially perforated domain with arbitrary density of cavities and mixed type conditions on their boundary. The corresponding spectral problem is also considered. A short communication of similar results can be found in [1].

On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes

Vincent Heuveline, Friedhelm Schieweck (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous P r - 1 -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound r * . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.

On the inhomogeneous nonlinear Schrödinger equation with harmonic potential and unbounded coefficient

Jianqing Chen (2010)

Czechoslovak Mathematical Journal

By deriving a variant of interpolation inequality, we obtain a sharp criterion for global existence and blow-up of solutions to the inhomogeneous nonlinear Schrödinger equation with harmonic potential i ϕ t = - ϕ + | x | 2 ϕ - | x | b | ϕ | p - 2 ϕ . We also prove the existence of unstable standing-wave solutions via blow-up under certain conditions on the unbounded inhomogeneity and the power of nonlinearity, as well as the frequency of the wave.

Currently displaying 441 – 460 of 693