|
| | | | |
| | | |
| Stat |
Members: 3665
Articles: 2'599'751
Articles rated: 2609
17 January 2025 |
|
| | | | |
|
Article overview
| |
|
|
A survey on the boundary behavior of the double layer potential in Schauder spaces in the frame of an abstract approach | | M. Lanza de Cristoforis
; | | Date: |
1 Sep 2023 | | Abstract: | We provide a summary of the continuity properties of the boundary integral
operator corresponding to the double layer potential associated to the
fundamental solution of a {em nonhomogeneous} second order elliptic
differential operator with constant coefficients in H"{o}lder and Schauder
spaces on the boundary of a bounded open subset of ${mathbb{R}}^n$.
The purpose is two-fold. On one hand we try present in a single paper all the
known continuity results on the topic with the best known exponents in a
H"{o}lder and Schauder space setting and on the other hand we show that many
of the properties we present can be deduced by applying results that hold in an
abstract setting of metric spaces with a measure that satisfies certain growth
conditions that include non-doubling measures as in a series of papers by
Garc’{i}a-Cuerva and Gatto in the frame of H"{o}lder spaces and later by the
author. | | Source: | arXiv, 2309.00393 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
REGISTER