Differential Equations

Schauder Estimates in Non-Linear Elliptic Equations

Event Date: Dec 11, 2014 in Differential Equations, Seminars

  Abstract: (también adjunto en pdf) In this talk we treat about conditions for which is possible to get C2,α estimates for solutions of second order, uniformly elliptic, fully non-linear equations: F(D2u,X) = f(X).  

Solutions to a supercritical elliptic problem

Event Date: Dec 04, 2014 in Differential Equations, Seminars

Optimizing the first nonzero Neumann eigenvalue on the cylinder

Event Date: Nov 06, 2014 in Differential Equations, Seminars

Abstract: In this talk, we will discuss the characterization of do- mains maximizing the first non-zero Neuman eivgenvalue on a general cylinder. We will also present our study of overdeter- mined problem which arises from the Hadamard formula for this eigenvalue.   A joint work with Tobias Weth.  

Interpolation inequalities: rigidity results, nonlinear flows and applications

Event Date: Nov 13, 2013 in Differential Equations, Seminars

Boundedness and regularity of isoperimetric sets with density

Event Date: Nov 06, 2013 in Differential Equations, Seminars

 Abstract: We show that every isoperimetric set in  $\R^N$ with density is bounded if the density is continuous and bounded by above and below. This improves the previously known boundedness results, which basically needed a Lipschitz assumption; on the other hand, the present assumption is sharp, as we show with an explicit example. To obtain our result, we observe that the main tool which is often used, namely a classical “$\epsilon-\epsilon$” property already discussed by Allard, Almgren and Bombieri, admits a weaker counterpart which is still sufficient for the boundedness,...

Asymptotic behaviour of solutions to relativistic Schrödinger equation and its applications.

Event Date: Nov 06, 2013 in Differential Equations, Seminars

 Abstract: We will discuss  about sharp asymptotic behaviour of solutions to relativistic Schrödinger equation together with  it’s applications to unique continuations properties (weak, strong, from sets of postive meassure) and sharp essentially self-adjointness of relativistic Schrödinger equation  with Coulomb potential.”