A priori bounds for positive solutions of subcritical elliptic equations

详细信息    查看全文

• 作者：Alfonso Castro ; Rosa Pardo
• 关键词：A priori estimates ; Positive solutions ; Subcritical nonlinearity ; Moving planes method ; Kelvin transform ; 35B45 ; 35B33 ; 35B09 ; 35J60
• 刊名：Revista Matem篓垄tica Complutense
• 出版年：2015
• 出版时间：September 2015
• 年：2015
• 卷：28
• 期：3
• 页码：715-731
• 全文大小：1,185 KB
• 参考文献：1.Atkinson, F.V., Peletier, L.A.: Elliptic equations with nearly critical growth. J. Differ. Equ. 70(3), 349鈥?65 (1987). doi:10.鈥?016/鈥?022-0396(87)90156-2 . (ISSN 0022-0396)MathSciNet View Article
  2.Bahri, A., Coron, J.M.: On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain. Commun. Pure Appl. Math. 41(3), 253鈥?94 (1988). doi:10.鈥?002/鈥媍pa.鈥?160410302 MathSciNet View Article MATH
  3.Brezis, H.: Functional analysis. Sobolev spaces and partial differential equations. In: Universitext. Springer, New York (2011). (ISBN 978-0-387-70913-0)
  4.Brezis, H., Turner, R.E.L.: On a class of superlinear elliptic problems. Commun. Part. Differ. Equ. 2(6), 601鈥?14 (1977). (ISSN 0360-5302)MathSciNet View Article MATH
  5.Castro, A., Pardo, R.: Branches of positive solutions of subcritical elliptic equations in convex domains. AIMS Proc. (to appear)
  6.Castro, A., Pardo, R.: Branches of positive solutions for subcritical elliptic equations. Progress Nonlinear Differ. Equ. Appl. (to appear) (contributions to nonlinear elliptic equations and systems: a tribute to Djairo Guedes de Figueiredo on the occasion of his 80th birthday)
  7.Castro, A., Shivaji, R.: Nonnegative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric. Commun. Part. Differ. Equ. 14(8鈥?), 1091鈥?100 (1989). doi:10.鈥?080/鈥?360530890882064鈥? . (ISSN 0360-5302)MathSciNet View Article MATH
  8.de Figueiredo, D.G., Lions, P.-L., Nussbaum, R.D.: A priori estimates and existence of positive solutions of semilinear elliptic equations. J. Math. Pures Appl. (9) 61(1), 41鈥?3 (1982). (ISSN 0021-7824)MathSciNet MATH
  9.Gidas, B., Spruck, J.: A priori bounds for positive solutions of nonlinear elliptic equations. Commun. Part. Differ. Equ. 6(8), 883鈥?01 (1981). doi:10.鈥?080/鈥?360530810882019鈥? . (ISSN 0360-5302)MathSciNet View Article MATH
  10.Gidas, B., Ni, W.M., Nirenberg, L.: Symmetry and related properties via the maximum principle. Commun. Math. Phys., 68(3), 209鈥?43 (1979) (ISSN 0010-3616). http://鈥媝rojecteuclid.鈥媜rg/鈥媑etRecord?鈥媔d=鈥媏uclid.鈥媍mp/鈥?103905359
  11.Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. In: Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol. 224, 2nd edn. Springer, Berlin (1983). (ISBN 3-540-13025-X)
  12.Han, Z.-C.: Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent. Ann. Inst. H. Poincar茅 Anal. Non Lin茅aire 8(2), 159鈥?74 (1991)MATH
  13.Joseph, D.D., Lundgren, T.S.: Quasilinear Dirichlet problems driven by positive sources. Arch. Rational Mech. Anal. 49, 241鈥?69 (1972/73)
  14.Ladyzhenskaya, O.A., Ural鈥檛seva, N.N.: Linear and Quasilinear Elliptic Equations. Academic Press, New York (1968). (translated from the Russian by Scripta Technica)MATH
  15.Lions, P.L.: On the existence of positive solutions of semilinear elliptic equations. SIAM Rev., 24(4). doi:10.鈥?137/鈥?024101 (theorem 2441鈥?67, 1982, ISSN 0036-1445)
  16.Nussbaum, R.: Positive solutions of nonlinear elliptic boundary value problems. J. Math. Anal. Appl. 51(2), 461鈥?82 (1975). (ISSN 0022-247x)MathSciNet View Article MATH
  17.Pohozaev, S.I.: On the eigenfunctions of the equation \({\varDelta }u+\lambda f(u)=0\) . Dokl. Akad. Nauk. SSSR 165, 36鈥?9 (1965)MathSciNet
  18.Serrin, J.: A symmetry problem in potential theory. Arch. Rational Mech. Anal. 43, 304鈥?18 (1971). (ISSN 0003-9527)MathSciNet View Article MATH
  19.Turner, R.E.L.: A priori bounds for positive solutions of nonlinear elliptic equations in two variables. Duke Math. J. 41, 759鈥?74 (1974). (ISSN 0012-7094)MathSciNet View Article MATH
  
• 作者单位：Alfonso Castro (1)
  Rosa Pardo (2)
  
  1. Department of Mathematics, Harvey Mudd College, Claremont, CA, 91711, USA
  2. Departamento de Matem谩tica Aplicada, Universidad Complutense de Madrid, 28040, Madrid, Spain
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  Applications of Mathematics
  Geometry
  Mathematics
  Topology
  
• 出版者：Springer Milan
• ISSN：1988-2807

文摘

We provide a-priori \(L^\infty \) bounds for positive solutions to a class of subcritical elliptic problems in bounded \(C^2\) domains. Our analysis widens the known ranges of subcritical nonlinearities for which positive solutions are a-priori bounded.