On the Poisson Equation on a Surface with a boundary condition in co-normal direction
This paper considers the existence of weak and strong solutions to the Poisson equation on a surface with a boundary condition in co-normal direction. We apply the Lax-Milgram theorem and some properties of $H^1$-functions to show the existence of a unique weak solution to the surface Poisson equati...
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | This paper considers the existence of weak and strong solutions to the
Poisson equation on a surface with a boundary condition in co-normal direction.
We apply the Lax-Milgram theorem and some properties of $H^1$-functions to show
the existence of a unique weak solution to the surface Poisson equation when
the exterior force belongs to $L_0^p$-space, where $H^1$- and $L_0^p$-
functions are the ones whose value of the integral over the surface equal to
zero. Moreover, we prove that the weak solution is a strong $L^p$-solution to
the system. As an application, we study the solvability of ${\rm{div}_\Gamma }
V = F$. The key idea of constructing a strong $L^p$-solution to the surface
Poisson equation with a boundary condition in co-normal direction is to make
use of solutions to the surface Poisson equation with a Dirichlet boundary
condition. |
---|---|
DOI: | 10.48550/arxiv.2209.06409 |