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Variational problems with concentration

Author: Martin Flucher
Publisher: Basel ; Boston : Birkhauser, ©1999.
Series: Progress in nonlinear differential equations and their applications, v. 36.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several  Read more...

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Additional Physical Format: Online version:
Flucher, Martin, 1962-
Variational problems with concentration.
Basel ; Boston : Birkhauser, ©1999
(OCoLC)812165098
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Martin Flucher
ISBN: 3764361360 9783764361365 0817661360 9780817661366
OCLC Number: 41674411
Description: viii, 163 pages : illustrations ; 24 cm.
Contents: 1 Introduction.- 2 P-Capacity.- 3 Generalized Sobolev Inequality.- 3.1 Local generalized Sobolev inequality.- 3.2 Critical power integrand.- 3.3 Volume integrand.- 3.4 Plasma integrand.- 4 Concentration Compactness Alternatives.- 4.1 CCA for critical power integrand.- 4.2 Generalized CCA.- 4.3 CCA for low energy extremals.- 5 Compactness Criteria.- 5.1 Anisotropic Dirichlet energy.- 5.2 Conformai metrics.- 6 Entire Extremals.- 6.1 Radial symmetry of entire extremals.- 6.2 Euler Lagrange equation (independent variable).- 6.3 Second order decay estimate for entire extremals.- 7 Concentration and Limit Shape of Low Energy Extremals.- 7.1 Concentration of low energy extremals.- 7.2 Limit shape of low energy extremals.- 7.3 Exploiting the Euler Lagrange equation.- 8 Robin Functions.- 8.1 P-Robin function.- 8.2 Robin function for the Laplacian.- 8.3 Conformai radius and Liouville's equation.- 8.4 Computation of Robin function.- 8.4.1 Boundary element method.- 8.4.2 Computation of conformai radius.- 8.4.3 Computation of harmonic centers.- 8.5 Other Robin functions.- 8.5.1 Helmholtz harmonic radius.- 8.5.2 Biharmonic radius.- 9 P-Capacity of Small Sets.- 10 P-Harmonic Transplantation.- 11 Concentration Points, Subconformai Case.- 11.1 Lower bound.- 11.2 Identification of concentration points.- 12 Conformai Low Energy Limits.- 12.1 Concentration limit.- 12.2 Conformai CCA.- 12.3 Trudinger-Moser inequality.- 12.4 Concentration of low energy extremals.- 13 Applications.- 13.1 Optimal location of a small spherical conductor.- 13.2 Restpoints on an elastic membrane.- 13.3 Restpoints on an elastic plate.- 13.4 Location of concentration points.- 14 Bernoulli's Free-boundary Problem.- 14.1 Variational methods.- 14.2 Elliptic and hyperbolic solutions.- 14.3 Implicit Neumann scheme.- 14.4 Optimal shape of a small conductor.- 15 Vortex Motion.- 15.1 Planar hydrodynamics.- 15.2 Hydrodynamic Green's and Robin function.- 15.3 Point vortex model.- 15.4 Core energy method.- 15.5 Motion of isolated point vortices.- 15.6 Motion of vortex clusters.- 15.7 Stability of vortex pairs.- 15.8 Numerical approximation of vortex motion.
Series Title: Progress in nonlinear differential equations and their applications, v. 36.
Responsibility: Martin Flucher.

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"This material is very rich, because various alternatives are possible. The book provides a good systematic overview of this difficult topic."--Zentralblatt Math

 
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