Alessandra Lunardi

Analytic semigroups and optimal regularity in parabolic problems

Introduction.- 0 Preliminary material: spaces of continuous and Holder continuous functions.- 1 Interpolation theory.- Analytic semigroups and intermediate spaces.- 3 Generation of analytic semigroups by elliptic operators.- 4 Nonhomogeneous equations.- 5 Linear parabolic problems.- 6 Linear nonautonomous equations.- 7 Semilinear equations.- 8 Fully nonlinear equations.- 9 Asymptotic behavior in fully nonlinear equations.- Appendix: Spectrum and resolvent.- Bibliography.- Index.

On the linear heat equation with fading memory

The linear heat equation in materials with memory is studied by reducing it to an abstract Volterra equation. Results of regularity, asymptotic behavior, and positivity are given.

Functional analytic methods for evolution equations

Preface.- Giuseppe Da Prato: An Introduction to Markov Semigroups.- Peer C. Kunstmann and Lutz Weis: Maximal

On the Ornstein-Uhlenbeck operator in ² spaces with respect to invariant measures

L_p -regularity for Parabolic Equations, Fourier Multiplier Theorems and

Nonautonomous Kolmogorov parabolic equations with unbounded coefficients

H^\infty

Cα-regularity for non-autonomous linear integrodifferential equations of parabolic type

-functional Calculus.- Irena Lasiecka: Optimal Control Problems and Riccati Equations for Systems with Unbounded Controls and Partially Analytic Generators-Applications to Boundary and Point Control Problems.- Alessandra Lunardi: An Introduction to Parabolic Moving Boundary Problems.- Roland Schnaubelt: Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations.

Global Solutions of Abstract Quasilinear Parabolic Equations

We consider a class of elliptic and parabolic differential operators with unbounded coefficients in Rn, and we study the properties of the realization of such operators in suitable weighted L2 spaces.

Dirichlet boundary conditions for elliptic operators with unbounded drift

We study a class of elliptic operators A with unbounded coeffi- cients defined in I × R d for some unbounded interval IR. We prove that, for any s 2 I, the Cauchy problem u(s,·) = f 2 Cb(R d ) for the parabolic equation Dtu = Au admits a unique bounded classical solution u. This allows to associate an evolution family {G(t, s)} with A, in a natural way. We study the main properties of this evolution family and prove gradient estimates for the function G(t, s)f. Under suitable assumptions, we show that there exists an evolution system of measures for {G(t, s)} and we study the first properties of the extension of G(t, s) to the L p -spaces with respect to such measures.

An interpolation method to characterize domains of generators of semigroups

Abstract Linear integrodifferential equations in general Banach space are studied and applications are given to linear integrodifferential partial differential equations.

Hypercontractivity and Asymptotic Behavior in Nonautonomous Kolmogorov Equations

Abstract Local and global existence and uniqueness for strict solutions of abstract quasilinear parabolic equations are studied. Applications to quasilinear parabolic partial differential equations are also given.