Strongly elliptic differential operators with (possibly) unbounded lower order coefficients are shown to generate C0-semigroups on L p (R N), 1 < p < +∞. An explicit characterization of the domain is given.
Let A : [0, τ ] → L(D, X) be strongly measurable and bounded, where D, X are Banach spaces such that D → X. We assume that the operator A(t) has maximal regularity for all t ∈ [0, τ ]. Then we show under some additional hypothesis (viz. relative continuity) that the non-autonomous problem (P) ˙ u + A(t)u = f a.e. the operators A(t) are accretive, we show… (More)
A continuum from neuronal cellular/subcellular properties to system processes appears to exist in many instances and to allow privileged approaches in neuroscience and neuropharmacology research. Brain signals and the cholinergic and GABAergic systems, in vivo and in vitro evidence from studies on the retina, or the "gamma band" oscillations in neuron… (More)
In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing C 1 function β with limr→+∞ β(r) < +∞. By using tools of optimal transport, we will show that this kind of problems is well posed in the class of nonnegative Borel… (More)
We prove sharp upper bounds for invariant measures of Markov processes in R N associated with second-order elliptic differential operators with unbounded coefficients.