The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.
While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning includeFlavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019)Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019)Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus, second edition (2020)Mariusz Lemańczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020)Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021)Miroslava Antić, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021)Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021)Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
By:
Jan H. Chabrowski
Imprint: De Gruyter
Country of Publication: Germany
Edition: Reprint 2011
Volume: 24
Dimensions:
Height: 248mm,
Width: 178mm,
Spine: 18mm
Weight: 625g
ISBN: 9783110152692
ISBN 10: 311015269X
Series: De Gruyter Studies in Mathematics
Pages: 299
Publication Date: 29 April 1997
Recommended Age: College Graduate Student
Audience:
Professional and scholarly
,
General/trade
,
Undergraduate
,
Undergraduate
,
Undergraduate
Format: Hardback
Publisher's Status: Active
Part 1 Constrained minimization: preliminaries; constrained minimization; dual method; minimizers with the least energy; application of dual method; multiple solutions of nonhomogeneous equation; sets of constraints; constrained minimization for Ff; subcritical problem; application to the p-Laplacian; critical problem. Part 2 Applications of Lusternik-Schnirelman theory: Palais-Smale condition, case p not equal to q; duality mapping; Palais-Smale condition, case p=q; the Lusternik-Schnirelman theory; case p>q; case pq; set of constraints V; application to a critical case p=n; technical lemmas; existence result for problem (3.34). Part 4 Potentials with covariance condition: preliminaries and constrained minimization; dual method; minimization subject to constraint V; Sobol inequality; mountain pass theorem and constrained minimization; minimization problem for a system of equations. Part 5 Eigenvalues and level sets: level sets; continuity and monotonicity of delta; the differentiability properties of delta; Schechters's version of the mountain pass theorem; general condition for solvability of (5.11); properties of the function K(t); Hilbert space case; application to elliptic equations. Part 6 Generalizations of the mountain pass theorem: version of a deformation lemma; mountain pass alternative; consequences of mountain pass alternative; Hampwile alternative; applicability of the mountain pass theorem; mountain pass and Hampwile alternative. Part 7 Nondifferentiable functionals: concept of a generalized gradient; generalized gradients in function spaces; mountain pass theorem for locally Lipschitz functionals; consequences of theorem 7.3.1; application to boundary value problems with discontinuous nonlinearity; lower semicontinuous perturbation; deformation lemma for functionals satisfying condition (L); application to variational inequalities. Part 8 Concentration-compactness principle - subcritical case: concentration-compactness principle at infinity - subcritical case; constrained minimization - subcritical case; constrained minimization b not equal const, subcritical case; behaviour of the Palais-Smale sequences; the exterior Dirichlet problem; the Palais-Smale condition; concentration-compactness principle 1. Part 9 Concentration-compactness principle - critical case: critical Sobolev exponent; concentration-compactness principle 2 - loss of mass at infinity; constrained minimization - critical case - Palais-Smale sequences in critica case; symmetric solutions; remarks on compact embeddings into L2*(Q) and L2*(R); appendix.
