Die klassisch-reguläre Lösbarkeit des Rand-Anfangswertproblems nichtlinearer Wellengleichungen mit einer Randbedingung vom gemischten Typ.
Differentiability and growth of solutions of partial differential equations.
Differentiability and partial Hölder continuity of the solutions of non-linear elliptic systems of order with quadratic growth
Dini continuity of the first derivatives of generalized solutions to the Dirichlet problem for linear elliptic second order equations in nonsmooth domains
We consider generalized solutions to the Dirichlet problem for linear elliptic second order equations in a domain bounded by a Dini-Lyapunov surface and containing a conical point. For such solutions we derive Dini estimates for the first order generalized derivatives.
Dini-Campanato spaces and applications to nonlinear elliptic equations.
Dirichlet problem for quasi-linear elliptic equations.
Dynamics of complex singularities in 1D nonlinear parabolic PDE's
We establish local-in-time smoothing of a simple model nonlinear parabolic PDE in a scale of weighted Bergman spaces on a strip provided the weights are not too singular. This constitutes a very strong smoothing property since an immediate consequence is that the PDE can "push away" an algebraic-type complex singularity provided that the order of the singularity is small enough.