# Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations

Luca Lorenzi ; Adbelaziz Rhandi

Semigroups of Bounded Operators and Second-Order Elliptic and Parabolic Partial Differential Equations aims to propose a unified
approach to elliptic and parabolic equations with bounded and smooth coefficients. Les mer

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Features

Useful for students and researchers as an introduction to the field of partial differential equations of elliptic and parabolic types

Introduces the reader to the theory of operator semigroups as a tool for the analysis of partial differential equations

1. Function spaces. I. Semigroups of bounded operators. 2. Strongly continuous semigroups. 3. Analytic semigroups. II. Parabolic
equations. 4. Elliptic and parabolic maximum principles. 5 Prelude to parabolic equations: the heat equation and the Gauss-Weierstrass
semigroup in C (Rd). 6. Parabolic equations in Rd. 7. Parabolic equations in Rd + with Dirichlet boundary conditions. 8. Parabolic
equations in Rd+ with more general boundary conditions. 9 Parabolic equations in bounded smooth domains . III Elliptic equations.
10. Elliptic equations in R . 11. Elliptic equations in Rd+ with homogeneous Dirichlet boundary conditions. 12. Elliptic equation
in Rd+ with general boundary conditions. 13 Elliptic equations on smooth domains . 14 Elliptic operators and analytic semigroups.
15. Kernel estimates. IV. Appendices. A Basic notion of Functional Analysis in Banach spaces. B Smooth domains and extension
operators.

Luca Lorenzi is Full Professor of Mathematical Analysis at University of Parma (Italy). He received his PhD in Mathematics
from the University of Pisa (Italy) in 2001. In 2000 he got a permanent position as assistant professor in Mathematical Analysis
at the University of Parma and he was promoted to associate professor in 2006 still at the University of Parma. In 2013 he
got the Italian National habilitation as full professor in Mathematical Analysis. His research interests are mainly focused
on Partial Differential Equations. In particular, Evolution Equations and Operator Semigroups, Non-autonomous Differential
Equations, Elliptic and Parabolic Differential Operators with Unbounded Coefficients. He has authored or co-authored over
60 papers published on international journals and three scientific monographs.

Abdelaziz Rhandi is Full Professor of Mathematical Analysis at University of Salerno (Italy). Before joining Salerno University in 2006, he served as Full Professor of Mathematics at the University of Marrakesh (Morocco) since 1999. He received his first PhD in Mathematics from the University of Besancon (France) and the second one from the University of Tubingen (Germany). In 2003, he got the Alexander von Humboldt Fellow and was the winner of the 2006 HP Technology for Teaching Higher Education Prize. He has worked as a visiting professor in several universities in Algeria, France, Germany, Italy, Tunisia and USA. His research interests are mainly focused on Applied Functional Analysis and Partial Differential Equations. In particular, Evolution Equations and Operator Semigroups, Non-autonomous Differential Equations, Elliptic and Parabolic Differential Operators with Unbounded Coefficients.

Abdelaziz Rhandi is Full Professor of Mathematical Analysis at University of Salerno (Italy). Before joining Salerno University in 2006, he served as Full Professor of Mathematics at the University of Marrakesh (Morocco) since 1999. He received his first PhD in Mathematics from the University of Besancon (France) and the second one from the University of Tubingen (Germany). In 2003, he got the Alexander von Humboldt Fellow and was the winner of the 2006 HP Technology for Teaching Higher Education Prize. He has worked as a visiting professor in several universities in Algeria, France, Germany, Italy, Tunisia and USA. His research interests are mainly focused on Applied Functional Analysis and Partial Differential Equations. In particular, Evolution Equations and Operator Semigroups, Non-autonomous Differential Equations, Elliptic and Parabolic Differential Operators with Unbounded Coefficients.