Page 482 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 482
GEOMETRIC-FUNCTIONAL INEQUALITIES AND RELATED TOPICS (MS-23)
Subelliptic geometric-functional inequalities
Durvudkhan Suragan, durvudkhan.suragan@nu.edu.kz
Nazarbayev University, Kazakhstan
In this talk, we discuss geometric-functional inequalities on stratified groups. In this environ-
ment, the theory of geometric-functional inequalities becomes intricately intertwined with the
properties of sub-Laplacians and more general subelliptic partial differential equations. Partic-
ularly, we discuss subelliptic Hardy-Sobolev type inequalities and their applications. Moreover,
we present sharp remainder terms for the higher-order Steklov inequality on stratified groups
which imply short and direct proofs of the sharp (classical) higher-order Steklov inequalities.
We also give representation formulae for the L2m-Friedrichs inequalities. This talk is partially
based on our recent works with Tohru Ozawa and Michael Ruzhansky.
An optimization problem in thermal insulation
Cristina Trombetti, cristina@unina.it
Università degli Studi di Napoli Federico II, Italy
We study thermal insulating of a bounded body. Under a prescribed heat source, we consider
a model of heat transfer between the body and the environment determined by convection; this
corresponds, before insulation, to Robin boundary conditions. We study the maximization of
heat content (which measures the goodness of the insulation) among all the possible distribu-
tions of insulating material with fixed mass, and prove an optimal upper bound in terms of
geometric properties. Eventually we prove a conjecture which states that the ball surrounded
by a uniform distribution of insulating material maximizes the heat content.
Characterization of Sobolev functions with zero traces via the distance
function from the boundary
Hana Turcˇinová, turcinova@karlin.mff.cuni.cz
Charles University, Czech Republic
Let Ω be a regular domain in the Euclidean space Rn and let d be the distance function from
the boundary of Ω. A classical result of late 1980’s states that for p ∈ (1, ∞) and m ∈ N,
u belongs to the Sobolev space W0m,p(Ω) if and only if u/dm ∈ Lp(Ω) and |∇mu| ∈ Lp(Ω).
During the consequent decades, several authors have spent considerable effort in order to relax
the characterizing condition concerning requirements on the regularity of the function u/dm.
We present a new such condition in terms of Lorentz spaces.
480
Subelliptic geometric-functional inequalities
Durvudkhan Suragan, durvudkhan.suragan@nu.edu.kz
Nazarbayev University, Kazakhstan
In this talk, we discuss geometric-functional inequalities on stratified groups. In this environ-
ment, the theory of geometric-functional inequalities becomes intricately intertwined with the
properties of sub-Laplacians and more general subelliptic partial differential equations. Partic-
ularly, we discuss subelliptic Hardy-Sobolev type inequalities and their applications. Moreover,
we present sharp remainder terms for the higher-order Steklov inequality on stratified groups
which imply short and direct proofs of the sharp (classical) higher-order Steklov inequalities.
We also give representation formulae for the L2m-Friedrichs inequalities. This talk is partially
based on our recent works with Tohru Ozawa and Michael Ruzhansky.
An optimization problem in thermal insulation
Cristina Trombetti, cristina@unina.it
Università degli Studi di Napoli Federico II, Italy
We study thermal insulating of a bounded body. Under a prescribed heat source, we consider
a model of heat transfer between the body and the environment determined by convection; this
corresponds, before insulation, to Robin boundary conditions. We study the maximization of
heat content (which measures the goodness of the insulation) among all the possible distribu-
tions of insulating material with fixed mass, and prove an optimal upper bound in terms of
geometric properties. Eventually we prove a conjecture which states that the ball surrounded
by a uniform distribution of insulating material maximizes the heat content.
Characterization of Sobolev functions with zero traces via the distance
function from the boundary
Hana Turcˇinová, turcinova@karlin.mff.cuni.cz
Charles University, Czech Republic
Let Ω be a regular domain in the Euclidean space Rn and let d be the distance function from
the boundary of Ω. A classical result of late 1980’s states that for p ∈ (1, ∞) and m ∈ N,
u belongs to the Sobolev space W0m,p(Ω) if and only if u/dm ∈ Lp(Ω) and |∇mu| ∈ Lp(Ω).
During the consequent decades, several authors have spent considerable effort in order to relax
the characterizing condition concerning requirements on the regularity of the function u/dm.
We present a new such condition in terms of Lorentz spaces.
480
