Friedrichs’ Extension Lemma with Boundary Values and Applications in Complex Analysis
نویسنده
چکیده
Abstract. Let Q be a first-order differential operator on a compact, smooth oriented Riemannian manifold with smooth boundary. Then, Friedrichs’ Extension Lemma states that the minimal closed extension Qmin (the closure of the graph) and the maximal closed extension Qmax (in the sense of distributions) of Q in L-spaces (1 ≤ p < ∞) coincide. In the present paper, we show that the same is true for boundary values with respect to Qmin and Qmax. This gives a useful characterization of weak boundary values. As an application, we derive the Bochner-MartinelliKoppelman formula for L-forms with weak ∂-boundary values.
منابع مشابه
Using finite difference method for solving linear two-point fuzzy boundary value problems based on extension principle
In this paper an efficient Algorithm based on Zadeh's extension principle has been investigated to approximate fuzzy solution of two-point fuzzy boundary value problems, with fuzzy boundary values. We use finite difference method in term of the upper bound and lower bound of $r$- level of fuzzy boundary values. The proposed approach gives a linear system with crisp tridiagonal coefficients matr...
متن کاملWater hammer simulation by explicit central finite difference methods in staggered grids
Four explicit finite difference schemes, including Lax-Friedrichs, Nessyahu-Tadmor, Lax-Wendroff and Lax-Wendroff with a nonlinear filter are applied to solve water hammer equations. The schemes solve the equations in a reservoir-pipe-valve with an instantaneous and gradual closure of the valve boundary. The computational results are compared with those of the method of characteristics (MOC), a...
متن کاملL2-transforms for boundary value problems
In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.
متن کاملNumerical error analysis for Evans function computations: a numerical gap lemma, centered-coordinate methods, and the unreasonable effectiveness of continuous orthogonalization
We perform error analyses explaining some previously mysterious phenomena arising in numerical computation of the Evans function, in particular (i) the advantage of centered coordinates for exterior product and related methods, and (ii) the unexpected stability of the (notoriously unstable) continuous orthogonalization method of Drury in the context of Evans function applications. The analysis ...
متن کاملDiscontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions
Discontinuous Galerkin Methods for Friedrichs Systems with Irregular Solutions Max Jensen Doctor of Philosophy Corpus Christi College Michaelmas Term 2004 This work is concerned with the numerical solution of Friedrichs systems by discontinuous Galerkin finite element methods (DGFEMs). Friedrichs systems are boundary value problems with symmetric, positive, linear first-order partial differenti...
متن کامل