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Abstrakty
We investigate a class of over-determined parabolic problems involving a non-constant boundary condition. The Weinstein's technique known for the elliptic problems is extended to the parabolic one by means of auxiliary functions and Green classical formula.
Wydawca
Czasopismo
Rocznik
Tom
Strony
235--247
Opis fizyczny
Bibliogr. 22 poz.
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autor
- Department of Mathematics. College of Sciences. King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia, radhkla @hotmail.com
Bibliografia
- [1] Brock, F., Henrot, A., A symmetry result for an overdetermined elliptic problem using continuous rearangement abd domain derivative, Rend. Circ. Mat. Palermo (2) 51 (2002), 375-390.
- [2] Dalmasso, R., Uniqueness theorems for some fourth order elliptic equations, Proc. Amer. Math. Soc. 123 (1995), 1177-1183.
- [3] Dalmasso, R., Uniqueness of positi'ue solutions for some fourth order nonlinear equations, J. Math. Anal. Appl. 201 (1996), 152-168.
- [4] Dalmasso, R., Existence and uniqueness of positive solutions of semilinear elliptic systems, Nonlinear Anal. 39 (2000), 559-568.
- [5] Friedman, A., Remarks on the maximum principle for parabolic equations and its applications, Pacific J. Math. 8 (1958), 201-211.
- [6] Greco, A., Monotonicity of solutions to some semilinear elliptic equations, Rend. Sem. Fac. Sci. Univ. Cagliari 65(1) (1995), 17-23.
- [7] Greco, A., Radial symmetry and uniqueness for an overdetermined problem, Math. Methods Appl. Sci. 24 (2001), 103-115.
- [8] Herirot, A., Philippin, G. A., On a class of over-determined eigenvalue problems, Math. Methods Appl. Sci. 20(11) (1997), 905-914.
- [9] Hopf, E., A remark on elliptic differential eqations of second order, Proc. Amer. Math. Soc. 3 (1952),791-793.
- [10] Hopf, E., Elementare Bemerkung ueber die Lueisung partieller Differentialgleichungen Zweiter Ordnung von elliptischen Typus, Berliner Sitzungsber. Preuss. Akad. Wiss. 19 (1927), 147-152.
- [11] Nirenberg, L., A strong maximum principle for parabolic equations, Comm. Pure Appl. Math. 6 (1953), 167-177.
- [12] Payne, L. E., Isoperimetric Inequalities, Maximum Pirciples and their Applications, Lecture Notes, Univ. of Newcastle, 1972.
- [13] Payne, L. E., Weinstein, A., Capacity virtual mass, and generalized symmetrization, Pacific J. Math. 2 (1952), 633-641.
- [14] Philippin, G. A., Ragoub, L., On some second order and fourth order elliptic over-determined problems, Z. Angew. Math. Phys. 46 (1995), 188-197.
- [15] Philippin, G. A., Safoui, A., Some overdetermined parabolic problems, Math. Methods Appl. Sci. 22(10) (1999), 791-799.
- [16] Protter, M. H., Weinberger, H. F., Maximum Principles in Differential Equations, Sringer-Verlag, New York, 1984.
- [17] Ragoub, L., Sur quelques problemes a, frontieres libres de type elliptique, These de l'Universite Laval, Quebec, Canada, 1996.
- [18] Serrin, J., A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304-318.
- [19] Sperb, R., Maximum Principles and their Applications, Math. Sci, Engrg. 157, Academic Press, Inc., New York-London, 1981.
- [20] Tewodros, A., Two symmetry problems in potential theory, Electron. J. Differential Equations 43 (2001), pp. 5 (electronic).
- [21] Weinberger, H. F., Remark on the preceding paper of Serrin, Arch. Rational Mech. Anal. 43 (1971), 319-320.
- [22] Weinstein, A., Generalized axially symmetric potential theory, Bull. Amer. Math. Soc. 59 (1952), 20-38.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0002-0039