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Beyond Bilinearity: Exploring Nonlinear Dirichlet Forms and their Applications

(Autor)

Buch | Softcover
172 Seiten
2024
tredition (Verlag)
978-3-384-26780-1 (ISBN)
CHF 40,95 inkl. MwSt
The main motivation and prime example of a Dirichlet form is the energy of the Laplace operator. The Laplacian was first introduced and studied by Laplace and other after him in the 18th and 19th century. Today the operator still is an active area of research, since it is of fundamental importance in the equations that govern heat, electromagnetism, uid motion and quantum mechanics. A modern approach, developed in the 20th century after the introduction of modern functional analysis in the form of Hilbert and Banach spaces, is the theory of semigroups and bilinear forms. The idea of semigroups goes back to von Neumann and his pivotal book on the mathematics of quantum mechanics [vN32]. He realised physical observable as self-adjoint operators and studied the groups generated by skew-selfadjoint Hamiltonians. Later on after the second world war, Hille [Hil48] as well as Phillips [LP61] established the general theory of strongly continuous semigroups and their generators. Let us sketch this approach for the Laplacian. Let a : H1(Rn) × H1(Rn) R be a bilinear form, defined by

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Erscheint lt. Verlag 21.6.2024
Verlagsort hyf
Sprache englisch
Maße 155 x 234 mm
Gewicht 299 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte Bilinearity • diffusion processes • Functional Analysis • Heat Kernel Methods • Markov Fields • Mathematics • Nonlinear Dirichlet Forms • Potential Theory • spectral theory • Stochastic Processes
ISBN-10 3-384-26780-X / 338426780X
ISBN-13 978-3-384-26780-1 / 9783384267801
Zustand Neuware
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