uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Quasi-linear PDEs and low-dimensional sets
University of Kentucky, Lexington, KY, USA.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2015 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863Article in journal (Refereed) Accepted
Abstract [en]

In this paper we establish new results concerning boundary Harnack inequalities and the Martin boundary problem, for non-negative solutions to equations of $p$-Laplace type with variable coefficients. The key novelty is that we consider solutions which vanish only on a low-dimensional set $\Sigma$ in $\mathbb R^n$ and this is different compared to the more traditional setting of boundary value problems set in the geometrical situation of a bounded domain in $\mathbb R^n$ having a boundary with (Hausdorff) dimension in the range $[n-1,n)$. We establish our  quantitative and scale-invariant estimates in the context of low-dimensional Reifenberg flat sets.

Place, publisher, year, edition, pages
National Category
URN: urn:nbn:se:uu:diva-260772OAI: oai:DiVA.org:uu-260772DiVA: diva2:848388
Available from: 2015-08-24 Created: 2015-08-24 Last updated: 2016-03-01

Open Access in DiVA

fulltext(579 kB)129 downloads
File information
File name FULLTEXT01.pdfFile size 579 kBChecksum SHA-512
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Nyström, Kaj
By organisation
Analysis and Probability Theory
In the same journal
Journal of the European Mathematical Society (Print)

Search outside of DiVA

GoogleGoogle Scholar
Total: 129 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 666 hits
ReferencesLink to record
Permanent link

Direct link