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There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes and the Morse inequalities.

Operatoren. --- Laplace-operatoren. --- Spectraaltheorie. --- Hypoelliptic operators. --- Spectral theory (Mathematics) --- Spectre (Mathématiques) --- Mathematics. --- Global analysis. --- Differential equations, partial. --- Quantum theory. --- Statistics. --- Partial Differential Equations. --- Global Analysis and Analysis on Manifolds. --- Quantum Physics. --- Statistics for Engineering, Physics, Computer Science, Chemistry & Geosciences. --- Hypoelliptic operators --- Mathematical Theory --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Operators, Hypoelliptic --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Partial differential equations --- Math --- Global analysis (Mathematics) --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Partial differential equations. --- Geometry. --- Quantum physics. --- Thermodynamics. --- Heat engineering. --- Heat transfer. --- Mass transfer. --- Engineering Thermodynamics, Heat and Mass Transfer. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Econometrics --- Science --- Mass transport (Physics) --- Thermodynamics --- Transport theory --- Heat transfer --- Thermal transfer --- Transmission of heat --- Energy transfer --- Heat --- Mechanical engineering --- Chemistry, Physical and theoretical --- Dynamics --- Mechanics --- Physics --- Heat-engines --- Quantum theory --- Euclid's Elements --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Engineering. --- Construction --- Industrial arts --- Technology --- Statistics . --- Partial differential operators --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics)

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"Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization.It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results.Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributorsAntunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartłomiej A., Velichkov Bozhidar

MATHEMATICS / Optimization.