eBook

Analysis of Heat Equations on Domains. (LMS-31)

Ouhabaz, El-Maati

2005

Overview

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 treatsLp 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 proveLp estimates for heat, Schrödinger, 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.

• Publisher: Princeton University Press
• Subject: Adjoint / Analytic semigroup / Approximation / Boundary value problem / Bounded operator / Boundedness / Cauchy problem / Characterization (mathematics) / Coefficient / Complex number / Convex set / Differential operator / Dirichlet boundary condition / Ellipse / Elliptic operator / Equation / Estimation / Euclidean space / Existential quantification / Functional analysis / Heat / Heat -- Transmission -- Measurement / 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 / MATHEMATICS / Applied / Measure (mathematics) / Measurement / Metric space / Mixed boundary condition / Neumann boundary condition / Open set / Partial differential equation / Peter Sarnak / Physics / Pointwise / Probabilities & applied mathematics / Probability / Resolvent set / Ricci curvature / Riemannian manifold / Riesz representation theorem / Riesz transform / SCIENCE / Physics / Mathematical & Computational / 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 / Transmission / Upper and lower bounds / Variable (mathematics) / Weight function
• ISBN: 9781400826483, 1400826489, 9780691120164, 0691120161