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Existence of solution to $p-$Kirchhoff type problem in $\mathbb{R}^N$ via Nehari manifold
Mirror symmetry for a Hessian over-determined problem and its generalization
1. | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
References:
[1] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, Serrin-type overdetermined problems: An alternative proof,, \emph{Arch. Rational Mech. Anal.}, 190 (2008), 267.
doi: 10.1007/s00205-008-0119-3. |
[2] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, On the stability of the Serrin problem,, \emph{J. Differ. Equ.}, 245 (2008), 1566.
doi: 10.1016/j.jde.2008.06.010. |
[3] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, Stability of radial symmetry for a Monge-Ampere overdetermined problem,, \emph{Annali di Matematica.}, 188 (2009), 445.
doi: 10.1007/s10231-008-0083-4. |
[4] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order equations IV. Starshaped compact Weingurtenhypersurfuces,, \emph{Current Topics Inpurtiul Differential Equations}, (1986), 1.
|
[5] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order elliptic equations V. The Dirichlet problem for Weingurten hypersurfuces,, \emph{Communications on Pure and Applied Mathematics}, 41 (1988), 47.
doi: 10.1002/cpa.3160410105. |
[6] |
L. E. Fraenkel, An introduction to Maximum Principles and Symmetry in Elliptic Problems,, Cambridge Tracts in Mathematics, (2000).
doi: 10.1017/CBO9780511569203. |
[7] |
B. Gidas, Weiming Ni and L. Nirenberg, Symmetry and related properties via the maximum principle,, \emph{Comm. Math. Phys.}, 68 (1979), 209.
|
[8] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, Second edition, (1983).
doi: 10.1007/978-3-642-61798-0. |
[9] |
B. Kawohl, Symmetrzationor how to prove symmetry of solutions to a PDE,, \emph{Partial differential equations} (Praha), (1998), 214.
|
[10] |
Congming Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains,, \emph{Comm. Partial Differential Equations}, 16 (1991), 585.
doi: 10.1080/03605309108820770. |
[11] |
W. Reichel, Radial symmetry for elliptic boundary-value problems on exterior domains,, \emph{Arch. Rational Mech. Anal.}, 137 (1997), 381.
doi: 10.1007/s002050050034. |
[12] |
W. Reichel, Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains,, \emph{Z. Anal. Anwendungen, 15 (1996), 619.
doi: 10.4171/ZAA/719. |
[13] |
J. Serrin, A symmetry problem in potential theory,, \emph{Arch. Rational Mech. Anal.}, 43 (1971), 304.
|
[14] |
H. Shahgholian, Diversifications of Serrin's and related symmetry problems,, \emph{Complex Variables and Elliptic Equations, 57 (2012), 653.
doi: 10.1080/17476933.2010.504848. |
[15] |
I. S. Sokolnikoff, Mathematical Theory of Elasticity,, McGraw-Hill, (1956).
|
[16] |
H. F. Weinberger, Remark on the preceding paper of Serrin,, \emph{Arch. Rational Mech. Anal.}, 43 (1971), 319.
|
show all references
References:
[1] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, Serrin-type overdetermined problems: An alternative proof,, \emph{Arch. Rational Mech. Anal.}, 190 (2008), 267.
doi: 10.1007/s00205-008-0119-3. |
[2] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, On the stability of the Serrin problem,, \emph{J. Differ. Equ.}, 245 (2008), 1566.
doi: 10.1016/j.jde.2008.06.010. |
[3] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, Stability of radial symmetry for a Monge-Ampere overdetermined problem,, \emph{Annali di Matematica.}, 188 (2009), 445.
doi: 10.1007/s10231-008-0083-4. |
[4] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order equations IV. Starshaped compact Weingurtenhypersurfuces,, \emph{Current Topics Inpurtiul Differential Equations}, (1986), 1.
|
[5] |
L. Caffarelli, L. Nirenberg and J. Spruck, Nonlinear second order elliptic equations V. The Dirichlet problem for Weingurten hypersurfuces,, \emph{Communications on Pure and Applied Mathematics}, 41 (1988), 47.
doi: 10.1002/cpa.3160410105. |
[6] |
L. E. Fraenkel, An introduction to Maximum Principles and Symmetry in Elliptic Problems,, Cambridge Tracts in Mathematics, (2000).
doi: 10.1017/CBO9780511569203. |
[7] |
B. Gidas, Weiming Ni and L. Nirenberg, Symmetry and related properties via the maximum principle,, \emph{Comm. Math. Phys.}, 68 (1979), 209.
|
[8] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, Second edition, (1983).
doi: 10.1007/978-3-642-61798-0. |
[9] |
B. Kawohl, Symmetrzationor how to prove symmetry of solutions to a PDE,, \emph{Partial differential equations} (Praha), (1998), 214.
|
[10] |
Congming Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains,, \emph{Comm. Partial Differential Equations}, 16 (1991), 585.
doi: 10.1080/03605309108820770. |
[11] |
W. Reichel, Radial symmetry for elliptic boundary-value problems on exterior domains,, \emph{Arch. Rational Mech. Anal.}, 137 (1997), 381.
doi: 10.1007/s002050050034. |
[12] |
W. Reichel, Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains,, \emph{Z. Anal. Anwendungen, 15 (1996), 619.
doi: 10.4171/ZAA/719. |
[13] |
J. Serrin, A symmetry problem in potential theory,, \emph{Arch. Rational Mech. Anal.}, 43 (1971), 304.
|
[14] |
H. Shahgholian, Diversifications of Serrin's and related symmetry problems,, \emph{Complex Variables and Elliptic Equations, 57 (2012), 653.
doi: 10.1080/17476933.2010.504848. |
[15] |
I. S. Sokolnikoff, Mathematical Theory of Elasticity,, McGraw-Hill, (1956).
|
[16] |
H. F. Weinberger, Remark on the preceding paper of Serrin,, \emph{Arch. Rational Mech. Anal.}, 43 (1971), 319.
|
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