Report 33/2005: Partial Differential Equations (Partielle Differentialgleichungen) (July 24th -- July 30th, 2005 (0530)) (Q870675)

Summary: The workshop dealt with partial differential equations in geometry and technical applications. The main topics were the combination of nonlinear partial differential equations and geometric measure theory, conformal invariance and the Willmore functional, and regularity of free boundaries. Contributions: \parindent=6mm \begin{itemize}\item[--]Leon Simon (joint with Neshan Wickramasekera), A PDE Construction of a Class of Stable Branched Minimal Immersions (p. 1871) \item[--]Ernst Kuwert (joint with Reiner Schätzle), An estimate for conformal surfaces with bounds on the Willmore energy (p. 1873) \item[--]Giuseppe Mingione (joint with Frank Duzaar, Erlangen and Jan Kristensen, Oxford), Singular sets of vectorial elliptic problems (p. 1875) \item[--]Valentino Magnani, Convexity in Carnot groups (p. 1877) \item[--]Oliver C. Schnürer, Expanding and contracting surfaces (p. 1882) \item[--]Mikhail Feldman (joint with Gui-Qiang Chen), Shock Reflection and Free Boundary Problems for Degenerate Elliptic Equations (p. 1885) \item[--]Michael Struwe, Concentration phenomena for Liouville's equation (p. 1886) \item[--]Matthew J. Gursky, A fully nonlinear version of the Yamabe problem (p. 1889) \item[--]Denis Labutin, Critical regularity for elliptic equations from Littlewood-Paley theory (p. 1890) \item[--]Guofang Wang (joint with J. Jost, C.-S. Lin), Analytic aspects of the Toda system (p. 1890) \item[--]Tobias Lamm, Forth order approximation of harmonic maps from surfaces (p. 1893) \item[--]Yoshihiro Tonegawa, Singular perturbation limit of phase separation problem (p. 1896) \item[--]Tatiana Toro (joint with Carlos Kenig), Two phase free boundary regularity problem for Harmonic measure and Poisson kernel (p. 1898) \item[--]Matthias Röger (joint with Reiner Schätzle), On a modified conjecture of De Giorgi (p. 1900) \item[--]Mohameden Ould Ahmedou, Multiplicity results for the prescribed Q-curvature (p. 1903) \item[--]Stefan Müller (joint with Maximilian Schultz), Convergence of equilibria of thin elastic films (p. 1905) \item[--]Gaven J. Martin, Beltrami Systems and the Hilbert-Smith Conjecture (p. 1908) \item[--]Andrea Malchiodi (joint with Jih-Hsin Cheng, Jenn-Fang Hwang and Paul Yang), Mean curvature and minimal surfaces in CR manifolds (p. 1910) \item[--]Darya Apushkinskaya, Regularity of free boundaries in parabolic obstacle type problems (p. 1913) \item[--]Neshan Wickramasekera, Regularity of stable branched minimal hypersurfaces (p. 1914) \item[--]Jens Frehse (joint with Sonja Goj and Mark Steinhauer), Lp-estimates for steady compressible fluids (p. 1918) \item[--]Paul Yang (joint with Alice Chang), Conformally Invariant differential equations on 4-manifolds (p. 1919) \item[--]Bernd Kirchheim (joint with M. Csörnyei, T. O'Neil, D. Preiss, S. Winter), Pure unrectifiability and universal singular sets in Tonelli's classical variational problem (p. 1922).\end{itemize}