Elliptic and Parabolic Equations

This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.

Résumé
The international workshop on which this proceedings volume is based on brought together leading researchers in the field of elliptic and parabolic equations. Particular emphasis was put on the interaction between well-established scientists and emerging young mathematicians, as well as on exploring new connections between pure and applied mathematics. The volume contains material derived after the workshop taking up the impetus to continue collaboration and to incorporate additional new results and insights.

Contenu

Uniformly regular and singular riemannian manifolds.- Eigenvalue estimates on Bakry-Emery manifolds.- A note on the local well-posedness for the Whitham equation.- On the lifetime of a conditioned Brownian motion in domains connected through small gaps.- Analyticity of rotational water waves.- Degenerate and singular porous medium type equations with measure data.- Aspects of the mathematical analysis of nonlinear stratified water waves.- A calculus of abstract edge pseudodifferential operators of type r;d.- Boundary value problems for elliptic wedge operators: the first order case.- The time singular limit for a fourth-order damped wave equation for MEMS.- Composition in the edge calculus.- On bifurcation for semilinear elliptic Dirichlet problems on shrinking domains.