Page 548 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 548
TOPICS IN SUB-ELLIPTIC AND ELLIPTIC PDES (MS-31)
Epsilon-regularity for p-harmonic maps at a free boundary on a sphere
Katarzyna Mazowiecka, katarzyna.mazowiecka@uclouvain.be
Université catholique de Louvain, Belgium
We prove an epsilon-regularity theorem for vector-valued p-harmonic maps, which are critical
with respect to a partially free boundary condition, namely that they map the boundary into a
round sphere. As a consequence we obtain partial regularity of stationary p-harmonic maps up
to the boundary away from a set of (n − p)-dimensional Hausdorff measure. Joint work with R.
Rodiac and A. Schikorra.
Monotone sets in Carnot groups: an interesting class of "convex" sets
Daniele Morbidelli, daniele.morbidelli@unibo.it
Università di Bologna, Italy
In this talk we discuss some properties of horizontal convexity in Carnot groups. Namely, in the
setting of a step-2 Carnot group G of rank at most 3, we show a classification of all sets E ⊂ G
which are horizontally convex and whose complement is convex too. Horizontal convexity is
relevant in the theory of second-order subelliptic pde and the monotonicity notion we discuss
here plays also a role in bilipschitz embeddability properties for subRiemannian spaces. This is
a joint paper with Séverine Rigot, from Nice.
A Resolution of the Poisson Problem for Elastic Plates
Francesco Palmurella, francesco.palmurella@math.ethz.ch
ETH Zürich, Switzerland
Coauthors: Francesca Da Lio, Tristan Rivière
The Poisson problem consists in finding a surface immersed in the Euclidean space minimising
Germain’s elastic energy (known as Willmore energy in geometry) with assigned boundary,
boundary Gauss map and area; it constitutes a non-linear model for the equilibrium state of
thin, clamped elastic plates. We present a solution, and discuss its partial boundary regularity,
to a variationally equivalent version of this problem when the boundary curve is simple and
closed, as in the most classical version of the Plateau problem. This is a Joint work with F. Da
Lio and T. Rivière.
Conformal fractional powers and heat kernels in Heisenberg-type groups
Giulio Tralli, giulio.tralli@unipd.it
University of Padova, Italy
In this talk we discuss the conformal fractional powers of the horizontal Laplacian in groups
of Heisenberg type. We present a new approach, based on the heat equation and on extension
operators, to the derivation of the fundamental kernels for these nonlocal operators and to the
construction of explicit solutions to fractional CR-Yamabe type problems. The talk is based on
joint works with N. Garofalo.
546
Epsilon-regularity for p-harmonic maps at a free boundary on a sphere
Katarzyna Mazowiecka, katarzyna.mazowiecka@uclouvain.be
Université catholique de Louvain, Belgium
We prove an epsilon-regularity theorem for vector-valued p-harmonic maps, which are critical
with respect to a partially free boundary condition, namely that they map the boundary into a
round sphere. As a consequence we obtain partial regularity of stationary p-harmonic maps up
to the boundary away from a set of (n − p)-dimensional Hausdorff measure. Joint work with R.
Rodiac and A. Schikorra.
Monotone sets in Carnot groups: an interesting class of "convex" sets
Daniele Morbidelli, daniele.morbidelli@unibo.it
Università di Bologna, Italy
In this talk we discuss some properties of horizontal convexity in Carnot groups. Namely, in the
setting of a step-2 Carnot group G of rank at most 3, we show a classification of all sets E ⊂ G
which are horizontally convex and whose complement is convex too. Horizontal convexity is
relevant in the theory of second-order subelliptic pde and the monotonicity notion we discuss
here plays also a role in bilipschitz embeddability properties for subRiemannian spaces. This is
a joint paper with Séverine Rigot, from Nice.
A Resolution of the Poisson Problem for Elastic Plates
Francesco Palmurella, francesco.palmurella@math.ethz.ch
ETH Zürich, Switzerland
Coauthors: Francesca Da Lio, Tristan Rivière
The Poisson problem consists in finding a surface immersed in the Euclidean space minimising
Germain’s elastic energy (known as Willmore energy in geometry) with assigned boundary,
boundary Gauss map and area; it constitutes a non-linear model for the equilibrium state of
thin, clamped elastic plates. We present a solution, and discuss its partial boundary regularity,
to a variationally equivalent version of this problem when the boundary curve is simple and
closed, as in the most classical version of the Plateau problem. This is a Joint work with F. Da
Lio and T. Rivière.
Conformal fractional powers and heat kernels in Heisenberg-type groups
Giulio Tralli, giulio.tralli@unipd.it
University of Padova, Italy
In this talk we discuss the conformal fractional powers of the horizontal Laplacian in groups
of Heisenberg type. We present a new approach, based on the heat equation and on extension
operators, to the derivation of the fundamental kernels for these nonlocal operators and to the
construction of explicit solutions to fractional CR-Yamabe type problems. The talk is based on
joint works with N. Garofalo.
546
