Die mathematische Optimierung von Vorgängen, die durch partielle Differentialgleichungen
modelliert werden, hat in den letzten Jahren einen beachtlichen Aufschwung genommen …

This research monograph is motivated by problems in mathematical physics that involve
fractional kinetic equations. These equations describe transport dynamics in complex …

For a linear, strictly elliptic second order differential operator in divergence form with
bounded, measurable coefficients on a Lipschitz domain Ω we show that solutions of the …

arxiv:0803.3179v2 [math.AP] 15 May 2008 Page 1 arxiv:0803.3179v2 [math.AP] 15 May 2008
GENERALIZED ROBIN BOUNDARY CONDITIONS, ROBIN-TO-DIRICHLET MAPS, AND …

In this paper we investigate the following fractional order in time Cauchy problem D t α u (t)+
A u (t)= f (u (t)), 1< α< 2, u (0)= u 0, u′(0)= u 1. The fractional in time derivative is taken in …

We develop a systematic theory of eventually positive semigroups of linear operators mainly
on spaces of continuous functions. By eventually positive we mean that for every positive …

The aim of this paper is twofold: First, we characterize an essentially optimal class of
boundary operators Θ which give rise to self-adjoint Laplacians− ΔΘ, Ω in L2 (Ω; dnx) with …

We give a simple proof of the Faber–Krahn inequality for the first eigenvalue of the p-
Laplace operator with Robin boundary conditions. The techniques introduced allow to work …

Using regularized resolvent families, we investigate the solvability of the fractional order
inhomogeneous Cauchy problem D _t^ α u (t)= Au (t)+ f (t),\; t> 0,\;\; 0< α ≤ 1, where …

A stabilization/observability estimate and asymptotic energy decay rates are derived for a
wave equation with nonlinear dam** in a portion of the interior and Wentzell condition on …