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Differential Equations and Function Spaces
Edited by: S. M. Nikol'skiĭ
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Proceedings of the Steklov Institute of Mathematics
1992; 256 pp; softcover
Volume: 192
ISBN-10: 0-8218-3146-1
ISBN-13: 978-0-8218-3146-5
List Price: US$208
Member Price: US$166.40
Order Code: STEKLO/192
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This commemorative volume honors the memory of S. L. Sobolev by presenting eighteen papers reflecting the area of Sobolev's main contributions: applications of functional analysis to differential equations. The papers examine various problems in the theory of partial differential equations (linear and nonlinear) and the theory of differentiable functions of several real variables. Applications to problems of mathematical physics and approximate methods of conformal mapping are also treated. Foreign (e.g., Leray, Lions, Fichera) as well as domestic (e.g., Besov, Oleĭnik, Il'in) authors are represented.

Readership

Researchers in differential equations familiar with applications of functional analysis.

Table of Contents

  • In Memory of Sergeĭ L'vovich Sobolev
  • N. S. Bakhvalov and M. Èglit -- Variational properties of averaged equations for periodic media
  • O. V. Besov -- On Sobolev-Liouville and Lizorkin-Triebel spaces on a domain
  • E. A. Volkov -- Approximate conformal mapping of the exterior of a lattice of ellipses onto the exterior of a lattice of plates by the block method
  • Yu. D. Golovatyĭ, S. A. Nazarov, and O. A. Oleĭnik -- Asymptotic expansions of eigenvalues and eigenfunctions in problems on oscillations of a medium with concentrated perturbations
  • Yu. V. Egorov and V. A. Kondrat'ev -- On the negative spectrum of an elliptic operator
  • V. P. Il'in -- On imbedding theory for anisotropic classes of functions with power smoothness and a metric of \(L_p\)-type
  • L. D. Kudryavtsev -- Variational problems with a different number of boundary conditions
  • G. P. Kheĭnig and A. Kufner -- Hardy's inequality for higher order derivatives
  • Zh. Lerè -- Le demi-plan élastique et la théorie des distributions
  • P. I. Lizorkin -- Classes of functions constructed on the basis of averages over spheres (the case of spaces of Sobolev type)
  • Zh. L. Lions -- On nonlinear sentinels for distributed systems
  • S. I. Pokhozhaev -- On the method of fibering a solution in nonlinear boundary value problems
  • S. G. Samko -- Hypersingular integrals and differences of fractional order
  • Sanches-Palensiya -- Some elasticity problems in unbounded domains and applications to junctions
  • V. N. Temlyakov -- On the behavior of the partial sums, over hyperbolic crosses, of Fourier series of periodic functions of several variables
  • G. Tribel' -- Characterizations of \(F^s_pq\) spaces via local means; the extension problem
  • S. V. Uspenskiĭ and E. M. Vasil'eva -- On the behavior at infinity of a solution of a problem in hydrodynamics
  • G. Fikera -- On the optimal constant for the trace inequality
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