Search Research Symposium Abstracts

Concentration of solutions to a system of nonlinear Schrödinger equations*

We consider a system of nonlinear elliptic equations that emerges as a model in various physical phenomena, for example, in the study of standing waves for a mixture of Bose-Einstein condensates of $\textit{m}$ hyperfine states that overlap in space. In the competitive case, that is, when the interaction between particles in the same state is attractive and [Read More...]

Presenter: Mónica Clapp, Universidad Nacional Autónoma de México
Authors: Mónica Clapp and Mayra Soares
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 18, 2022; 3:20 pm

Shape evolution of geometric curvature flow and nonlocal interaction interfaces*

In this survey talk, we present the recent progress of studying a class of minimal geometric partial differential equations to understand the evolution of boundaries between states in pattern-forming [Read More...]

Presenter: Eun Heui Kim, California State University, Long Beach
Authors: James von Brecht, Scott McCalla, Eun Heui Kim
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 18, 2022; 3:45 pm

Regularity of Free Boundaries

In this talk we will review the problem of regularity for the free boundary problem first introduced by Alt, Caffarelli, and Friedman. We will discuss several recent results about this problem in the case of Neumann fixed [Read More...]

Presenter: Sarah Raynor, Wake Forest University
Authors: Sarah Raynor
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 18, 2022; 4:10 pm

On oscillatory nonlinearities in different elliptic equations

I will present some results concerning existence of positive solutions to some elliptic problems with oscillatory nonlinearities, either at the interior or at the boundary. We present suficient conditions for a bifurcation from infinity phenomenon, and we prove the existence of infinitely many resonant solutions, of infinitely many stable solutions, of [Read More...]

Presenter: Prof. Rosa Pardo, Universidad Complutense de Madrid
Authors: B. Delgado, M. Chetri, N. Mavinga, R. Pardo
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 18, 2022; 4:35 pm

Two solutions on a Nehari set in an invariant cone*

In this talk, we will discuss the existence and variational characterization of two distinct non-constant, radial, radially nondecreasing solutions to a $p$-Laplacian problem set in a ball of $\bf{R}^N,$ under Neumann boundary conditions. The problem involves a power nonlinearity, which is supercritical in the sense of Sobolev embeddings, and the power $p$, [Read More...]

Presenter: Francesca Colasuonno, Università di Bologna
Authors: F. Colasuonno, B. Noris, G. Verzini
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 19, 2022; 8:50 am

Mutiplicity of solutions for almost critical elliptic problems via Orlicz spaces approach*

We study the existence of positive solutions of a Dirichlet problem for a class of semilinear superlinear elliptic equations whose nonlinear term is of subcritical nature in a generalized sense and involves indefinite nonlinearities. More precisely, given Ω ⊂ R^N , N > 2, a bounded, connected open subset with C^2 boundary ∂Ω, we look for positive [Read More...]

Presenter: Mabel Cuesta, Université du Littoral Côte d'Opale (ULCO), Calais (France)
Authors: Mabel Cuesta and Rosa Pardo
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 19, 2022; 9:15 am

Strongly singular problems in exterior domains*

Singular problems arise in the study of non-Newtonian fluids, boundary layer phenomena for viscous fluids, chemical heterogeneous catalysts, as well as in the theory of heat conduction in electrically conducting materials. An increasing attention to singular stationary or evolution equations has been paid in the last decades. In the present talk we deal [Read More...]

Presenter: Francesca Faraci, University of Catania, Italy
Authors: Maya Chhetri, Francesca Faraci
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 19, 2022; 9:40 am

A Sharp Divergence Theorem with Non-Tangential Traces

The Integration by Parts Formula, which is equivalent with the Divergence Theorem, is one of the most basic tools in Analysis. Originating in the works of Gauss, Ostrogradsky, and Stokes, the search for an optimal version of this fundamental result continues through this day and these efforts have been the driving force in shaping up entire sub-branches of [Read More...]

Presenter: IRINA MITREA, Temple University
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 19, 2022; 10:05 am

Discussion

There are relatively few women working in Nonlinear PDEs, especially in the United States. We will have a short discussion at the end of our session where we will brainstorm ideas to recruit women in the field, and ways to mentor [Read More...]

Presenter: Nsoki Mavinga, Swarthmore College
Symposium Year: 2022
Session: Advances in Nonlinear Partial Differential Equations
Presentation Time: June 19, 2022; 10:30 am