Citation: |
[1] |
A. D. Alexandrov, A characteristic property of the sphere, Ann. Mat. Pura Appl., 58 (1962), 303-354. |
[2] |
L. Barbu and C. Enache, A maximum principle for some fully nonlinear elliptic equations with applications to Weingarten surfaces, Complex Var. Elliptic Equ., 58 (2013), 1725-1736. |
[3] |
B. Brandolini, C. Nitsch, P. Salani and C. Trombetti, Serrin type overdetermined problems : An alternative proof, Arch. Ration. Mech. Anal., 190 (2008), 267-280.doi: 10.1007/s00205-008-0119-3. |
[4] |
L. A. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet Problem for Nonlinear Second-Order Elliptic Equations I. Monge-Ampère Equation, Comm. Pure App. Math., 37 (1984), 369-402.doi: 10.1002/cpa.3160370306. |
[5] |
C. Enache, Maximum principles and symmetry results for a class of fully nonlinear elliptic PDEs, NODEA - Nonlinear Differ. Equ. Appl., 17 (2010), 591-600.doi: 10.1007/s00030-010-0070-5. |
[6] |
C. Enache, Necessary conditions of solvability and isoperimetric estimates for some Monge-Ampère problems in the plane, Proc. Amer. Math. Soc., to appear. |
[7] |
E. Hopf, Elementare Bemerkung über die Lösung partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus, Berlin Sber. Preuss. Akad. Wiss, 19 (1927), 147-152. |
[8] |
E. Hopf, A remark on linear elliptic differential equations of the second order, Proc. Amer. Math. Soc., 36 (1952), 791-793. |
[9] |
H. Hopf, Differential geometry in the large: seminar lectures New York University 1946 and Stanford University 1956, vol. 1000 of Lecture Notes in Mathematics, Springer Verlag, 1989. |
[10] |
N. M. Ivochkina, Solution of the Dirichlet problem for equations of mth order curvature, (Russian) Mat. Sb., 180 (1989), 867-887; translation in Math. USSR-Sb., 67 (1990), 317-339. |
[11] |
P. L. Lions, N. S. Trudinger and J. Urbas, The Neumann problem for equations of Monge-Ampère type, Comm. Pure Appl. Math., 39 (1986), 539-563.doi: 10.1002/cpa.3160390405. |
[12] |
X.-N. Ma, A necessary condition of solvability for the capillarity boundary of Monge-Ampère equations in two dimensions, Proc. Amer. Math. Soc., 127 (1999), 763-769.doi: 10.1090/S0002-9939-99-04750-4. |
[13] |
X.-N. Ma, Sharp size estimates for capillary free surfaces without gravity, Pacific J. Math., 192 (2000), 121-134.doi: 10.2140/pjm.2000.192.121. |
[14] |
L. E. Payne and G. A. Philippin, Some maximum principles for nonlinear elliptic equations in divergence form with applications to capillary surfaces and to surfaces of constant mean curvature, Nonlinear Anal., 3 (1979), 193-211.doi: 10.1016/0362-546X(79)90076-2. |
[15] |
G. A. Philippin, A minimum principle for the problem of torsional creep, J. Math. Anal. Appl., 68 (1979), 526-535.doi: 10.1016/0022-247X(79)90133-1. |
[16] |
G. A. Philippin and A. Safoui, Some maximum principles and symmetry results for a class of boundary value problems involving the Monge-Ampère equation, Math. Models Meth. Appl. Sci., 11 (2001), 1073-1080.doi: 10.1142/S0218202501001240. |
[17] |
G. A. Philippin and A. Safoui, Some applications of the maximum principle to a variety of fully nonlinear elliptic PDE's, Z. angew. Math. Phys., 54 (2003), 739-755.doi: 10.1007/s00033-003-3200-7. |
[18] |
G. A. Philippin and A. Safoui, Some minimum principles for a class of elliptic boundary value problems, Appl. Anal., 83 (2004), 231-241.doi: 10.1080/00036810310001632754. |
[19] |
H. Rosenberg, Hypersurfaces of constant curvature in space forms, Bull. Sci. Math., 117 (1993), 211-239. |
[20] |
J. Serrin, A symmetry problem in potential theory, Arch. Ration. Mech. Anal., 43 (1971), 304-318. |
[21] |
R. P. Sperb, Maximum Principles and Their Applications, Academic Press, (1981). |
[22] |
J. Urbas, Nonlinear oblique boundary value problem for Hessian equations in two dimensions, Ann. Inst. Henri Poincare, 12 (1995), 507-575. |
[23] |
J. Urbas, A note on the contact angle boundary condition for Monge-Ampère equations, Proc. Amer. Math. Soc., 128 (2000), 853-855.doi: 10.1090/S0002-9939-99-05222-3. |
[24] |
H. F. Weinberger, Remarks on the preceding paper of Serrin, Arch. Ration. Mech. Anal., 43 (1971), 319-320. |