Stochastic integration in Banach spaces and applications to parabolic evolution equations

Stochastic partial differential equations (SPDEs) of evolution type are usually modelled as ordinary stochastic differential equations (SDEs) in an infinite-dimensional state space. In many examples such as the stochastic heat and wave equation, this viewpoint may lead to existence and uniqueness results and regularity properties. To model the...

Higher order elliptic problems and positivity

The main subject of this thesis concerns positivity for fourth order elliptic problems. By positivity we mean that a positive source term in the differential equation leads to a positive solution. For second order elliptic partial differential equations such a result is known and referred to by the name maximum principle. It is also well known...

An analytic semigroup approach to convolution Volterra equations

Unconditional decompositions and multiplier theorems

Semilinear elliptic systems of FitzHugh-Nagumo type

On functional calculi for closed linear operators

Quasilinear Evolution Problems

Semigroups of operators: Approximation and saturation in banach spaces