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Tytuł artykułu

Weinstein's technique for a class of parabolic problems

Autorzy
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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
Rocznik
Strony
235--247
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
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
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