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Dirichlet problems without convexity assumption

Aleksandra Orpel (2005)

Annales Polonici Mathematici

We deal with the existence of solutions of the Dirichlet problem for sublinear and superlinear partial differential inclusions considered as generalizations of the Euler-Lagrange equation for a certain integral functional without convexity assumption. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principles which enables approximation of the solution for our problem.

Dirichlet-Neumann alternating algorithm for an exterior anisotropic quasilinear elliptic problem

Baoqing Liu, Qikui Du (2014)

Applications of Mathematics

In this paper, by the Kirchhoff transformation, a Dirichlet-Neumann (D-N) alternating algorithm which is a non-overlapping domain decomposition method based on natural boundary reduction is discussed for solving exterior anisotropic quasilinear problems with circular artificial boundary. By the principle of the natural boundary reduction, we obtain natural integral equation for the anisotropic quasilinear problems on circular artificial boundaries and construct the algorithm and analyze its convergence....

Discontinuous elliptic problems in ℝ N without monotonicity assumptions

Silvia Cingolani, Monica Lazzo (2001)

Commentationes Mathematicae Universitatis Carolinae

We prove existence of a positive, radial solution for a semilinear elliptic problem with a discontinuous nonlinearity. We use an approximating argument which requires no monotonicity assumptions on the nonlinearity.

Discontinuous Galerkin methods for problems with Dirac delta source∗

Paul Houston, Thomas Pascal Wihler (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement ...

Discontinuous Galerkin methods for problems with Dirac delta source∗

Paul Houston, Thomas Pascal Wihler (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement ...

Discontinuous quasilinear elliptic problems at resonance

Nikolaos Kourogenis, Nikolaos Papageorgiou (1998)

Colloquium Mathematicae

In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.

Discrete approximations of generalized RBSDE with random terminal time

Katarzyna Jańczak-Borkowska (2012)

Discussiones Mathematicae Probability and Statistics

The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.

Discrete maximum principle for interior penalty discontinuous Galerkin methods

Tamás Horváth, Miklós Mincsovics (2013)

Open Mathematics

A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of...

Discrete Sobolev inequalities and L p error estimates for finite volume solutions of convection diffusion equations

Yves Coudière, Thierry Gallouët, Raphaèle Herbin (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The topic of this work is to obtain discrete Sobolev inequalities for piecewise constant functions, and to deduce L p error estimates on the approximate solutions of convection diffusion equations by finite volume schemes.

Dispersive estimates and absence of embedded eigenvalues

Herbert Koch, Daniel Tataru (2005)

Journées Équations aux dérivées partielles

In [2] Kenig, Ruiz and Sogge proved ∥ u ∥ L 2 n n - 2 ( ℝ n ) ≲ ∥ L u ∥ L 2 n n + 2 ( ℝ n ) provided n ≥ 3 , u ∈ C 0 ∞ ( ℝ n ) and L is a second order operator with constant coefficients such that the second order coefficients are real and nonsingular. As a consequence of [3] we state local versions of this inequality for operators with C 2 coefficients. In this paper we show how to apply these local versions to the absence of embedded eigenvalues for potentials in L n + 1 2 and variants thereof.

Currently displaying 61 – 80 of 109