Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Analytic solutions for the classical two-phase Stefan problem
Positivity and Regularity of Hyperbolic Volterra Equations in Banach Spaces.
A Note on Strict Solutions to Semilinear Evolution Equations.
On semilinear evolution equations in Banach spaces.
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal -regularity is shown. By means of this purely operator theoretic approach, classical results on -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface...
Completely positive measures and Feller semigroups.
Global existence for a semilinear prabolic Volterra equation.
On Operators with Bounded Imaginary Powers in Banach Spaces.
Analysis of the boundary symbol for the two-phase Navier-Stokes equations with surface tension
The two-phase free boundary value problem for the Navier-Stokes system is considered in a situation where the initial interface is close to a halfplane. We extract the boundary symbol which is crucial for the dynamics of the free boundary and present an analysis of this symbol. Of particular interest are its singularities and zeros which lead to refined mapping properties of the corresponding operator.
The domain of the Ornstein-Uhlenbeck operator on an -space with invariant measure
We show that the domain of the Ornstein-Uhlenbeck operator on equals the weighted Sobolev space , where is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.
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