- Library Home /
- Search Collections /
- Open Collections /
- Browse Collections /
- BIRS Workshop Lecture Videos /
- Minkowski Inequality and nonlinear potential theory...
Open Collections
BIRS Workshop Lecture Videos
BIRS Workshop Lecture Videos
Minkowski Inequality and nonlinear potential theory (part 1) Mazzieri, Lorenzo
Description
In this talk, we first recall how some monotonicity formulas can be derived along the level set flow of the capacitary potential associated with a given bounded domain $\Omega$. A careful analysis is required in order to preserve the monotonicity across the singular times, leading in turn to a new quantitative version of the Willmore inequality. Remarkably, such analysis can be carried out without any \emph{a priori} knowledge of the size of the singular set. Hence, the same order of ideas applies to the $p$-capacitary potential of $\Omega$, whose critical set, for $p\neq2$, is not necessarily negligible. In this context, a generalised version of the Minkowski inequality is deduced. Joint works with M. Fogagnolo and L. Mazzieri.
Item Metadata
Title |
Minkowski Inequality and nonlinear potential theory (part 1)
|
Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
|
Date Issued |
2019-05-06T16:06
|
Description |
In this talk, we first recall how some monotonicity formulas
can be derived along the level set flow of the
capacitary potential associated with a given bounded domain $\Omega$.
A careful analysis is required in order to preserve
the monotonicity across the singular times,
leading in turn to a new
quantitative version of the Willmore inequality.
Remarkably, such analysis can be carried out
without any \emph{a priori}
knowledge of the size of the singular set.
Hence, the same order of ideas
applies to the $p$-capacitary potential
of $\Omega$, whose critical set, for $p\neq2$,
is not necessarily negligible.
In this context, a generalised version
of the Minkowski
inequality is deduced.
Joint works with M. Fogagnolo and L. Mazzieri.
|
Extent |
31.0 minutes
|
Subject | |
Type | |
File Format |
video/mp4
|
Language |
eng
|
Notes |
Author affiliation: Università di Trento
|
Series | |
Date Available |
2019-11-03
|
Provider |
Vancouver : University of British Columbia Library
|
Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
|
DOI |
10.14288/1.0384901
|
URI | |
Affiliation | |
Peer Review Status |
Unreviewed
|
Scholarly Level |
Researcher
|
Rights URI | |
Aggregated Source Repository |
DSpace
|
Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International