Nonlinear Analysis Seminar
Nonlinear Analysis and PDEs
CUNY Graduate Center, 365 Fifth Avenue, NYC
Room 4214.03
Goal of this seminar is to discuss techniques that can be used to tackle nonlinear
problems arising in applied mathematics, physics or differential geometry.
It will also give the opportunity of learning some recent progress in these fields.
Fall 2026
September 24th, 2:00pm-3:30pm (in person):
TBA
Abstract:
October (in person):
TBA
Abstract:
Spring 2026
March 19th (in person):
Samuel Magill (CUNY Graduate Center)
Variational Sub-super method in some PDE problems with singularities
Abstract:
The sub-super method to detect a solution to nonlinear problems has been reconsidered by Struwe in a variational context.
I will discuss how it can be refined, and discuss how it can be applied to find some solutions for a class of problems
that involve Dirac measures.
April 16th (in person):
Inigo Urtiaga Erneta (Rutgers University)
Regularity of oblique transmission problems
Abstract:
I will discuss transmission problems model phenomena in domains made up of multiple adjacent phases.
While a variational ``divergence-form'' theory for such problems is by now classical, a non-variational approach has only emerged recently.
This talk concerns the regularity of viscosity solutions to such transmission problems in non-divergence form.
I will present new results in the case of flat interfaces, where the transmission condition
is allowed to depend on both the normal and tangential derivatives of the solution.
This condition can be interpreted as a nonlinear coupling of oblique derivatives from each side of the interface.
Our main result establishes optimal piecewise Hölder regularity of viscosity solutions.
April 23rd, at 5:30pm (in person):
Thesis Defense of Samuel Magill
Variational methods for semilinear PDEs with Dirac Singularities
Abstract:
We consider semilinear elliptic PDEs in two dimensions involving Dirac measures.
Using a sub- and supersolution method designed for variational problems introduced by Struwe,
we will present some new results for different classes of PDEs.
We will first cover the case of some PDEs with exponential nonlinearity subjected to Dirichlet boundary condition,
and then discuss a broad class of problems on the torus that arise from some vortex condensation models. The method does not rely on a monotone iteration scheme or maximum principle arguments allowing it to extend naturally to coupled systems.
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