Autovalores do Laplaciano - Departamento de Matemática - UFMG
Autovalores do Laplaciano - Departamento de Matemática - UFMG Autovalores do Laplaciano - Departamento de Matemática - UFMG
Rodney Josué Biezuner 155 [GWW2] Carolyn GORDON, David L. WEBB e Scott WOLPERT, Isospectral plane domains and surfaces via Riemannian orbifolds, Inventiones Mathematicae 110 (1992), n. 1, 1–22. [Hackbusch] W. HACKBUSCH, Elliptic Differential Equations: Theory and Numerical Treatment, Springer Series in Computational Mathematics 18, Springer, 1992. [Herrman] H. HERRMANN, Beziehungen zwischen den Eigenwerten und Eigenfunktionen verschiedener Eigenwertprobleme, Math. Z. 40 (1935), 221–241. [Heuveline] Vincent HEUVELINE, On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods, Journal of Computational Physics 184 (2003), 321–337. [Horn-Johnson] Roger A. HORN e Charles R. JOHNSON, Matrix Analysis, Cambridge University Press, 1985. [Johnson] Claes JOHNSON, Numerical solutions of partial differential equations by the finite element method, Cambridge, 1987. [Jost] Jürgen JOST, Partial Differential Equations, Graduate Texts in Mathematics 214, Springer-Verlag, 2002. [Kac] M. KAC, Can one hear the shape of a drum?, American Mathematical Monthly 73 (1966), no. 4, part II, 1–23. [Kuttler-Sigillito] J. R. KUTTLER e V. G. SIGILLITO, Eigenvalues of the Laplacian in two dimensions, SIAM REVIEW 26 (1984) no. 2, 163–193. [Milnor] J. MILNOR, Eigenvalues of the Laplace operator on certain manifolds, Proceedings of the National Academy of Sciences USA 51 (1964), 542. [Pleijel] A. PLEIJEL, Remarks on Courant’s nodal line theorem, Comm. Pure Appl. Math. 9 (1956), 543–550. [Protter] M. H. PROTTER, Can one hear the shape of a drum? Revisited, SIAM REVIEW 29 (1987) no. 2, 185–197. [Rosser1] J. Barkley ROSSER, Nine point difference solutions for Poisson’s equation, Comp. Math. Appl. 1 (1975), 351–360. [Rosser2] J. Barkley ROSSER, Finite-difference solution of Poisson’s equation in rectangles of arbitrary proportions, Zeitschrift für Angewandte Mathematik und Physik (ZAMP) 28 (1977), no.2, 185–196. [Sridhar-Kudrolli] S. SRIDAR e A. KUDROLLI, Experiments on not “hearing the shape” of drums, Physical Review Letters 72 (1994), 2175–2178. [Strang] Gilbert STRANG, Linear Algebra and its Applications, 3rd Ed., Harcourt Brace Jovanovich, 1988. [Strikwerda] John C. STRIKWERDA, Finite Difference Schemes and Partial Differential Equations, 2nd Ed., SIAM, 2004. [Thomas1] J. W. THOMAS, Numerical Partial Differential Equations: Finite Difference Methods, Texts in Applied Mathematics 22, Springer, 1995.
Rodney Josué Biezuner 156 [Thomas2] J. W. THOMAS, Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations, Texts in Applied Mathematics 33, Springer, 1999. [Uhlenbeck1] K. UHLENBECK, Eigenfunctions of Laplace operator, Bulletin of the American Mathematical Society 78 (1972), 1073–1076. [Uhlenbeck2] K. UHLENBECK, Generic properties of eigenfunctions, American Journal of Mathematics 98 (1976), 1059–1078. [Vigneras] Marie-France VIGNÉRAS, Varietés riemanniennes isospectrales et non isometriques, Annals of Mathematics 91 (1980), 21–32. [Wat1] K. WATANABE, Plane Domains Which Are Spectrally Determined, Annals of Global Analysis and Geometry 18 (2000), no. 5, 447–475. [Wat2] K. WATANABE, Plane Domains Which Are Spectrally Determined II, J. Inequal. Appl. 7 (2002), no. 1, 25–47. [Watkins] David S. WATKINS, Fundamentals of Matrix Computations, 2nd Ed., John Wiley & Sons, 2002. [Weyl] H. WEYL, Über die Asymptotische Verteilung der Eigenwerte, Nachr. Konigl. Ges. Wiss. Göttingen (1911), 110–117. [Young] David M. YOUNG, Iterative Solutions of Large Linear Systems, Academic Press, 1971. [Zelditch] S. ZELDITCH, Spectral determination of analytic bi-axisymmetric plane domains, Geometric and Functional Analysis 10 (2000), no. 3, 628–677.
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- Page 155: Referências Bibliográficas [Asmar
Rodney Josué Biezuner 155<br />
[GWW2] Carolyn GORDON, David L. WEBB e Scott WOLPERT, Isospectral plane <strong>do</strong>mains<br />
and surfaces via Riemannian orbifolds, Inventiones Mathematicae 110 (1992), n. 1,<br />
1–22.<br />
[Hackbusch] W. HACKBUSCH, Elliptic Differential Equations: Theory and Numerical Treatment,<br />
Springer Series in Computational Mathematics 18, Springer, 1992.<br />
[Herrman] H. HERRMANN, Beziehungen zwischen <strong>de</strong>n Eigenwerten und Eigenfunktionen verschie<strong>de</strong>ner<br />
Eigenwertprobleme, Math. Z. 40 (1935), 221–241.<br />
[Heuveline] Vincent HEUVELINE, On the computation of a very large number of eigenvalues for<br />
selfadjoint elliptic operators by means of multigrid methods, Journal of Computational<br />
Physics 184 (2003), 321–337.<br />
[Horn-Johnson] Roger A. HORN e Charles R. JOHNSON, Matrix Analysis, Cambridge University<br />
Press, 1985.<br />
[Johnson] Claes JOHNSON, Numerical solutions of partial differential equations by the finite<br />
element method, Cambridge, 1987.<br />
[Jost] Jürgen JOST, Partial Differential Equations, Graduate Texts in Mathematics 214,<br />
Springer-Verlag, 2002.<br />
[Kac] M. KAC, Can one hear the shape of a drum?, American Mathematical Monthly 73<br />
(1966), no. 4, part II, 1–23.<br />
[Kuttler-Sigillito] J. R. KUTTLER e V. G. SIGILLITO, Eigenvalues of the Laplacian in two dimensions,<br />
SIAM REVIEW 26 (1984) no. 2, 163–193.<br />
[Milnor] J. MILNOR, Eigenvalues of the Laplace operator on certain manifolds, Proceedings<br />
of the National Aca<strong>de</strong>my of Sciences USA 51 (1964), 542.<br />
[Pleijel] A. PLEIJEL, Remarks on Courant’s nodal line theorem, Comm. Pure Appl. Math. 9<br />
(1956), 543–550.<br />
[Protter] M. H. PROTTER, Can one hear the shape of a drum? Revisited, SIAM REVIEW<br />
29 (1987) no. 2, 185–197.<br />
[Rosser1] J. Barkley ROSSER, Nine point difference solutions for Poisson’s equation, Comp.<br />
Math. Appl. 1 (1975), 351–360.<br />
[Rosser2] J. Barkley ROSSER, Finite-difference solution of Poisson’s equation in rectangles of<br />
arbitrary proportions, Zeitschrift für Angewandte Mathematik und Physik (ZAMP)<br />
28 (1977), no.2, 185–196.<br />
[Sridhar-Kudrolli] S. SRIDAR e A. KUDROLLI, Experiments on not “hearing the shape” of drums,<br />
Physical Review Letters 72 (1994), 2175–2178.<br />
[Strang] Gilbert STRANG, Linear Algebra and its Applications, 3rd Ed., Harcourt Brace Jovanovich,<br />
1988.<br />
[Strikwerda] John C. STRIKWERDA, Finite Difference Schemes and Partial Differential Equations,<br />
2nd Ed., SIAM, 2004.<br />
[Thomas1] J. W. THOMAS, Numerical Partial Differential Equations: Finite Difference Methods,<br />
Texts in Applied Mathematics 22, Springer, 1995.
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