Analysis of Heat Equations on Domains. (LMS-31)
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A01=El-Maati Ouhabaz
Adjoint
Analytic semigroup
Approximation
Author_El-Maati Ouhabaz
Boundary value problem
Bounded operator
Boundedness
C0
Category=PBKJ
Category=PH
Cauchy problem
Characterization (mathematics)
Coefficient
Complex number
Convex set
Differential operator
Dirichlet boundary condition
Ellipse
Elliptic operator
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
eq_science
Equation
Estimation
Euclidean space
Existential quantification
Functional analysis
Heat equation
Heat kernel
Hermitian adjoint
Hilbert space
Inverse trigonometric functions
Invertible matrix
Irreducibility (mathematics)
Lebesgue measure
Lie group
Linearity
Lp space
Martin Bridson
Mathematical physics
Mathematics
Measure (mathematics)
Metric space
Mixed boundary condition
Neumann boundary condition
Open set
Partial differential equation
Peter Sarnak
Pointwise
Probability
Resolvent set
Ricci curvature
Riemannian manifold
Riesz representation theorem
Riesz transform
Self-adjoint
Self-adjoint operator
Semigroup
Sesquilinear form
Sign (mathematics)
Singular integral
Smoothness
Sobolev inequality
Special case
Spectral theory
Square root
Stochastic calculus
Theorem
Theory
Time derivative
Upper and lower bounds
Variable (mathematics)
Weight function
Product details
- ISBN 9780691120164
- Weight: 510g
- Dimensions: 152 x 235mm
- Publication Date: 31 Oct 2004
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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This is the first comprehensive reference published on heat equations associated with non self-adjoint uniformly elliptic operators. The author provides introductory materials for those unfamiliar with the underlying mathematics and background needed to understand the properties of heat equations. He then treats Lp properties of solutions to a wide class of heat equations that have been developed over the last fifteen years. These primarily concern the interplay of heat equations in functional analysis, spectral theory and mathematical physics. This book addresses new developments and applications of Gaussian upper bounds to spectral theory. In particular, it shows how such bounds can be used in order to prove Lp estimates for heat, Schrodinger, and wave type equations. A significant part of the results have been proved during the last decade. The book will appeal to researchers in applied mathematics and functional analysis, and to graduate students who require an introductory text to sesquilinear form techniques, semigroups generated by second order elliptic operators in divergence form, heat kernel bounds, and their applications.
It will also be of value to mathematical physicists. The author supplies readers with several references for the few standard results that are stated without proofs.
El-Maati Ouhabaz is Professor of Analysis and Geometry at Universite Bordeaux 1
