On Courant's nodal domain theorem

Forum Mathematicum

Volumn 10, Issue 5, 1998, Pages 521-532

  Alessandrini, Giovanni ^a  

^a UNIVERSITY OF TRIESTE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032381645     PISSN: 09337741     EISSN: None     Source Type: Journal    
DOI: 10.1515/form.10.5.521     Document Type: Article

References (14)

1. Aronszajn, N., Krzywicki, A. and Szarski, J.: A unique continuation theorem for exterior differential forms on Riemannian manifolds. Ark. Mat. 4 (1962), 417-453
2. Alessandrini, G. and Magnanini, R.: Elliptic equations in divergence form geometric critical points of solutions and Stekloff eigenvalues. SIAM J. Math. Anal. 25(5) (1994), 1259-1268
3. Bérard, P. and Meyer, D.: Inégalités isopérimétriques et applications. Ann. Sci. Ecole Norm. Sup. 15 (1982), 513-542
4. Bers, L. and Nirenberg, L.: On a representation theorem for linear elliptic systems with discontinuous coefficients and its applications; in "Convegno Internazionale sulle Equazioni alle Derivate Parziali", Cremonese, Roma 1955
5. Chavel, I.: Eigenvalues in Riemannian Geometry. Academic Press, Orlando 1984
6. Courant, R. and Hilbert, D.: Methods of Mathematical Phisics vol. I. Interscience, New York 1953
7. Finn, R. and Gilbarg, D.: Asymptotic behaviour and uniqueness of plane subsonic flows. Comm. Pure Appl. Math. 10 (1957), 23-63
8. Gilbarg, D. and Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order. Second edition, Springer, Berlin 1983
9. Herrmann, H.: Beziehungen zwischen den Eigenwerten und Eigenfunktionen verschiedener Eigenwertprobleme. Math. Z. 40 (1935), 221-241
10. Littman, W., Stampacchia, G. and Weinberger, H.: Regular points for elliptic equations with discontinuous coefficients. Ann. Scuola Norm. Sup. Pisa (3)17 (1963), 43-77
11. Miller, K.: Nonunique continuation for uniformly parabolic and elliptic equations in self-adjoint divergence form with Holder continuous coefficients. Arch. Rational Mech. Anal. 54 (1974), 105-117
12. Miller, K.: Total total internal reflection; in P. Marcellini, G. Talenti, E. Vesentini eds., "Partial Differential Equations and Applications", Marcel Dekker, New York 1996
13. Pleijel, A.: Remarks on Courant's nodal line theorem. Comm. Pure Appl. Math. 9 (1956), 543-550
14. Pliś, A.: On non-uniqueness in Cauchy problem for an elliptic second order differential equation. Bull. Acad. Polon. Ser. Sci. Math. Astron. Phys. 11 (1963), 95-100