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1.

図書

図書
E.B. Dynkin
出版情報: Providence, R.I. : American Mathematical Society, c2002  xi, 236 p. ; 26 cm
シリーズ名: Colloquium publications / American Mathematical Society ; v. 50
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Introduction Parabolic equations and branching exit
Markov systems: Linear parabolic equations and diffusions
Branching exit Markov systems Superprocesses Semilinear parabolic equations and superdiffusions
Elliptic equations and diffusions: Linear elliptic equations and diffusions
Positive harmonic functions Moderate solutions of $Lu=\psi(u)$ Stochastic boundary values of solutions
Rough trace Fine trace Martin capacity and classes $\mathcal{N}_1$ and $\mathcal{N}_0$ Null sets and polar sets
Survey of related results Basic facts of Markov processes and Martingales Facts on elliptic differential equations
Epilogue
Bibliography
Subject index
Notation index
Introduction Parabolic equations and branching exit
Markov systems: Linear parabolic equations and diffusions
Branching exit Markov systems Superprocesses Semilinear parabolic equations and superdiffusions
2.

図書

図書
E.M. Landis ; [translated by Tamara Rozhkovskaya]
出版情報: Providence, R.I. : American Mathematical Society, c1998  xii, 203 p. ; 27 cm
シリーズ名: Translations of mathematical monographs ; v. 171
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Elliptic equations in nondivergence form
Elliptic equations in divergence form
Parabolic equations
Appendix
Bibliography
Index
Elliptic equations in nondivergence form
Elliptic equations in divergence form
Parabolic equations
3.

図書

図書
by Yakov Roitberg
出版情報: Dordrecht ; Boston, Mass. : Kluwer Academic, c1999  x, 276 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 498
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4.

図書

図書
Abduhamid Dzhuraev
出版情報: Boca Raton, FL : Chapman & Hall/CRC, c2000  195 p. ; 25 cm
シリーズ名: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 109
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5.

図書

図書
Bert-Wolfgang Schulze, Boris Sternin, Victor Shatalov
出版情報: Berlin ; Chichester : Wiley-VCH, c1998  376 p. ; 25 cm
シリーズ名: Mathematical topics ; v. 15
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6.

図書

図書
L.E. Fraenkel
出版情報: Cambridge ; New York : Cambridge University Press, 2000  x, 340 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 128
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Preface
Some notation, terminology and basic calculus / 0:
Introduction / 1:
Some maximum principles for elliptic equations / 2:
Symmetry for a non-linear Poisson equation / 3:
Symmetry for the non-linear Poisson equation in RN / 4:
Monotonicity of positive solutions in a bounded set W / 5:
On the Newtonian potential / Appendix A:
Rudimentary facts about harmonic functions and the Poisson equation / Appendix B:
Construction of the primary function of Siegel type / Appendix C:
On the divergence theorem and related matters / Appendix D:
The edge-point lemma / Appendix E:
Notes on sources
References
Index
Preface
Some notation, terminology and basic calculus / 0:
Introduction / 1:
7.

図書

図書
V.A. Kozlov, V.G. Mazʹya, J. Rossmann
出版情報: Providence, R.I. : American Mathematical Society, c1997  ix, 414 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 52
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Introduction
Boundary value problems for ordinary differential equations on the half-axis / Part 1:
Elliptic boundary value problems in the half-space
Elliptic boundary value problems in smooth domains
Variants and extensions
Elliptic boundary value problems in an infinite cylinder / Part 2:
Elliptic boundary value problems in domains with conical points
Elliptic boundary value problems in weighted
Sobolev spaces with nonhomogeneous norms
Elliptic boundary value problems in domains with exterior cusps / Part 3:
Elliptic boundary value problems in domains with inside cusps
Bibliography
Index
List of symbols
Introduction
Boundary value problems for ordinary differential equations on the half-axis / Part 1:
Elliptic boundary value problems in the half-space
8.

図書

図書
Heinrich G.W. Begehr and Guo Chun Wen
出版情報: Harlow, Essex, England : Longman, c1996  269 p. ; 25 cm
シリーズ名: Pitman monographs and surveys in pure and applied mathematics ; 80
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9.

図書

図書
А.Ф. Шестопал
出版情報: Киев : Наукова думка, 1968  208 p. ; 21 cm
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10.

図書

図書
Olaf Steinbach
出版情報: Berlin ; Tokyo : Springer, c2003  vi, 120 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1809
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目次情報: 続きを見る
Introduction
Preliminaries / 1:
Sobolev Spaces / 1.1:
Saddle Point Problems / 1.2:
Finite Element Spaces / 1.3:
Projection Operators / 1.4:
Quasi Interpolation Operators / 1.5:
Stability Results / 2:
Piecewise Linear Elements / 2.1:
Dual Finite Element Spaces / 2.2:
Higher Order Finite Element Spaces / 2.3:
Biorthogonal Basis Functions / 2.4:
The Dirichlet-Neumann Map for Elliptic Boundary Value Problems / 3:
The Steklov-Poincaré Operator / 3.1:
The Newton potential / 3.2:
Approximation by Finite Element Methods / 3.3:
Approximation by Boundary Element Methods / 3.4:
Mixed Discretization Schemes / 4:
Variational Methods with Approximate Steklov-Poincaré Operators / 4.1:
Lagrange Multiplier Methods / 4.2:
Hybrid Coupled Domain Decomposition Methods / 5:
Dirichlet Domain Decomposition Methods / 5.1:
A Two-Level Method / 5.2:
Three-Field Methods / 5.3:
Neumann Domain Decomposition Methods / 5.4:
Numerical Results / 5.5:
Concluding Remarks / 5.6:
References
Introduction
Preliminaries / 1:
Sobolev Spaces / 1.1:
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