25 citations · 97 across the 23 of their papers we have counts for
16 papers · 1 filter
The Perron solution for elliptic equations without the maximum principle
W. Arendt, A. F. M. ter Elst, M. Sauter
In this article we consider the Dirichlet problem on a bounded domain with respect to a second-order elliptic differential operator in divergence form. We do n…
The Wentzell Laplacian via forms and the approximative trace
Wolfgang Arendt, Manfred Sauter
We use form methods to define suitable realisations of the Laplacian on a domain with Wentzell boundary conditions, i.e. such that holds…
Semilinear elliptic equations on rough domains
Wolfgang Arendt, Daniel Daners
The paper makes use of recent results in the theory of Banach lattices and positive operators to deal with abstract semilinear equations. The aim is to work with minimal or no regu…
Strict positivity for the principal eigenfunction of elliptic operators with various boundary conditions
Wolfgang Arendt, A. F. M. ter Elst, Jochen Glück
We consider elliptic operators with measurable coefficients and Robin boundary conditions on a bounded domain and show that the first eigenfunction sati…
Operators with continuous kernels
W. Arendt, A. F. M. ter Elst
Let be open. We investigate conditions under which an operator on has a continuous kernel . In the centre…
Maximal -regularity in nonlinear gradient systems and perturbations of sublinear growth
Wolfgang Arendt, Daniel Hauer
The nonlinear semigroup generated by the subdifferential of a convex lower semicontinuous function has a smoothing effect, discovered by H. Brézis, which implies maximal regula…