USF Home > College of Arts and Sciences > Department of Mathematics & Statistics

Mathematics & Statistics

(Leader:

**Title**

**Speaker**

**Time**

**Place**

Randomness in the Heisenberg group

Diego Ricciotti

12:30pm-1:30pm

CMC 109

**Abstract**

We discuss some stochastic processes and their relation to Brownian motion and PDEs in the Heisenberg group.

**Title**

**Speaker**

**Time**

**Place**

A new proof for the equivalence of weak and viscosity solutions for the \(p\)-Laplace and the \(p(x)\)-Laplace equation in \(R^n\)

Robert Freeman

12:30pm-1:30pm

CMC 109

**Abstract**

The equivalence of weak and viscosity solutions in \(R^n\) was given by Juutinen, Lindqvist, and Manfredi in 2001. In this talk we will examine the new proof of the equivalence for the \(p\)-Laplace equation in \(R^n\) via infimal convolutions given by Julin and Juutinen in 2012. We will also discuss the strategies/difficulties in extending this proof to the \(p(x)\)-Laplace equation in R^n as well as the Heisenberg group.

**Title**

**Speaker**

**Time**

**Place**

Tug of war games and the p-Laplacian in the Heisenberg group

Diego Ricciotti

12:30pm-1:30pm

CMC 109

**Abstract**

We discuss a game theoretic interpretation of \(p\)-harmonic functions by exploiting the connection between PDEs, mean value properties and dynamic programming principles. In particular we obtain an approximation scheme at a discrete level, and we prove uniform convergence to the solution of the associated Dirichlet problem with continuous boundary datum, under suitable regularity assumptions of the domain.

**Title**

**Speaker**

**Time**

**Place**

Equivalence of weak and viscosity solutions to the \(p(x)\)-Laplace equation in Carnot groups

Robert Freeman

12:30pm-1:30pm

CMC 109

**Abstract**

We will discuss the known Euclidean results and new results in Carnot groups of the equivalence of weak and viscosity solutions to the \(p(x)\)-Laplace equation.

No seminar this week due to Spring Break.

**Title**

**Speaker**

**Time**

**Place**

Nonlinear potential theory, Part 1

Thomas Bieske

12:30pm-1:30pm

CMC 109

**Abstract**

We discuss various topics in nonlinear potential theory from Heinonen-Kilpelainen-Martio such as \(A_p\) weights, quasiconformal mappings and capacity of sets.

**Title**

**Speaker**

**Time**

**Place**

Plates with incompatible prestrain and non-euclidean elasticity

Diego Ricciotti

12:30pm-1:30pm

CMC 109

**Abstract**

We examine a model (coming from non-Euclidean elasticity) for thin plates that become internally prestrained in the absence of external forces or imposed boundary conditions. Examples of this phenomena occur in nature for instance in growing leaves or tissues. We describe a derivation of a 2D model arising as \(\Gamma\)-limit of a 3D model as the thickness parameter approaches zero, under appropriate scalings of the energy in terms of the plate's thickness.

**Title**

**Speaker**

**Time**

**Place**

Sub-Riemannian Geometry and Partial Differential Equations, Part IV

Thomas Bieske

12:30pm-1:30pm

CMC 109

**Title**

**Speaker**

**Time**

**Place**

Sub-Riemannian Geometry and Partial Differential Equations, Part III

Thomas Bieske

12:30pm-1:30pm

CMC 109

**Title**

**Speaker**

**Time**

**Place**

Sub-Riemannian Geometry and Partial Differential Equations, Part II

Thomas Bieske

12:30pm-1:30pm

CMC 109

**Title**

**Speaker**

**Time**

**Place**

Sub-Riemannian Geometry and Partial Differential Equations

Thomas Bieske

12:30pm-1:30pm

CMC 109

**Abstract**

We examine properties of solutions to the eikonal and infinite Laplace equations in sub-Riemannian spaces. The interplay between the underlying geometry and these solutions will also be explored.