3 papers
math.AP2025
Variational solutions of the Dirichlet problem, Lebesgue's cusp and non-local properties
Wolfgang Arendt, Daniel Daners, Manfred Sauter
A recent result from [AtES24] allows one to define variational solutions of the Dirichlet problem for general continuous boundary data. We establish basic properties of this notion…
math.AP2025
Elliptic systems generating a positive semigroup are decoupled
Wolfgang Arendt, A. F. M. ter Elst, Manfred Sauter
We show that the semigroup associated to a second-order elliptic system is positive if and only if the differential equations are essentially decoupled and the coefficients are rea…
math.AP2025
Maximal regularity for generalized boundary conditions in time
Wolfgang Arendt, Manfred Sauter
We consider autonomous and non-autonomous evolution equations on a time interval in a Banach space with the non-standard time-boundary condition , where…