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Polyharmonic Kirchhoff type equations with singular exponential nonlinearities
A new proof of gradient estimates for mean curvature equations with oblique boundary conditions
1. | University of Science and Technology of China, Hefei Anhui, 230026, China |
References:
[1] |
L. A. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations III: Functions of the eigenvalues of the Hessian,, \emph{Acta Math.}, 155 (1985), 261.
doi: 10.1007/BF02392544. |
[2] |
C. Gerhardt, Global regularity of the solutions to the capillary problem,, \emph{Ann. Scuola Norm. Sup. Pisa Cl. Sci.}, 3 (1976), 157.
|
[3] |
P. F. Guan and X. N. Ma, The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equations,, \emph{Invent. Math.}, 151 (2003), 553.
doi: 10.1007/s00222-002-0259-2. |
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, 2$^{nd}$ edition, (2001).
|
[5] |
N. J. Korevaar, Maximum principle gradient estimates for the capillary problem,, \emph{Comm. in Partial Differential Equations}, 13 (1988), 1.
doi: 10.1080/03605308808820536. |
[6] |
G. M. Lieberman, The conormal derivative problem for elliptic equations of variational type,, \emph{J.Differential Equations}, 49 (1983), 218.
doi: 10.1016/0022-0396(83)90013-X. |
[7] |
G. M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations,, \emph{Nonlinear Analysis. Theory. Method $ & $ Applications}, 8 (1984), 49.
doi: 10.1016/0362-546X(84)90027-0. |
[8] |
G. M. Lieberman, Gradient bounds for solutions of nonuniformly elliptic oblique derivative problems,, \emph{Nonlinear Anal.}, 11 (1987), 49.
doi: 10.1016/0362-546X(87)90025-3. |
[9] |
G. M. Lieberman, Gradient estimates for capillary-type problems via the maximum principle,, \emph{Commun. in Partial Differential Equations}, 13 (1988), 33.
doi: 10.1080/03605308808820537. |
[10] |
G. M. Lieberman, Oblique Boundary Value Problems for Elliptic Equations,, World Scientific Publishing Co. Pte. Ltd., (2013).
doi: 10.1142/8679. |
[11] |
X. N. Ma and J. J. Xu, Gradient estimates of mean curvature equations with Neumann boundary condition,, \emph{Advances in Mathematics}, 290 (2016), 1010.
doi: 10.1016/j.aim.2015.10.031. |
[12] |
L. Simon and J. Spruck, Existence and regularity of a capillary surface with prescribed contact angle,, \emph{Arch. Rational Mech. Anal.}, 61 (1976), 19.
|
[13] |
J. Spruck, On the existence of a capillary surface with prescribed contact angle,, \emph{Comm. Pure Appl. Math.}, 28 (1975), 189.
|
[14] |
N. S. Trudinger, The Dirichlet problem for the prescribed curvature equations,, \emph{Arch. Rational Mech. Anal.}, 111 (1990), 153.
doi: 10.1007/BF00375406. |
[15] |
N. N. Ural'tseva, The solvability of the capillary problem,, \emph{(Russian) Vestnik Leningrad. Univ. No. 19 Mat. Meh. Astronom.Vyp.}, 4 (1973), 54.
|
[16] |
X. J. Wang, Interior gradient estimates for mean curvature equations,, \emph{Math.Z.}, 228 (1998), 73.
doi: 10.1007/PL00004604. |
show all references
References:
[1] |
L. A. Caffarelli, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second order elliptic equations III: Functions of the eigenvalues of the Hessian,, \emph{Acta Math.}, 155 (1985), 261.
doi: 10.1007/BF02392544. |
[2] |
C. Gerhardt, Global regularity of the solutions to the capillary problem,, \emph{Ann. Scuola Norm. Sup. Pisa Cl. Sci.}, 3 (1976), 157.
|
[3] |
P. F. Guan and X. N. Ma, The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equations,, \emph{Invent. Math.}, 151 (2003), 553.
doi: 10.1007/s00222-002-0259-2. |
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order,, 2$^{nd}$ edition, (2001).
|
[5] |
N. J. Korevaar, Maximum principle gradient estimates for the capillary problem,, \emph{Comm. in Partial Differential Equations}, 13 (1988), 1.
doi: 10.1080/03605308808820536. |
[6] |
G. M. Lieberman, The conormal derivative problem for elliptic equations of variational type,, \emph{J.Differential Equations}, 49 (1983), 218.
doi: 10.1016/0022-0396(83)90013-X. |
[7] |
G. M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations,, \emph{Nonlinear Analysis. Theory. Method $ & $ Applications}, 8 (1984), 49.
doi: 10.1016/0362-546X(84)90027-0. |
[8] |
G. M. Lieberman, Gradient bounds for solutions of nonuniformly elliptic oblique derivative problems,, \emph{Nonlinear Anal.}, 11 (1987), 49.
doi: 10.1016/0362-546X(87)90025-3. |
[9] |
G. M. Lieberman, Gradient estimates for capillary-type problems via the maximum principle,, \emph{Commun. in Partial Differential Equations}, 13 (1988), 33.
doi: 10.1080/03605308808820537. |
[10] |
G. M. Lieberman, Oblique Boundary Value Problems for Elliptic Equations,, World Scientific Publishing Co. Pte. Ltd., (2013).
doi: 10.1142/8679. |
[11] |
X. N. Ma and J. J. Xu, Gradient estimates of mean curvature equations with Neumann boundary condition,, \emph{Advances in Mathematics}, 290 (2016), 1010.
doi: 10.1016/j.aim.2015.10.031. |
[12] |
L. Simon and J. Spruck, Existence and regularity of a capillary surface with prescribed contact angle,, \emph{Arch. Rational Mech. Anal.}, 61 (1976), 19.
|
[13] |
J. Spruck, On the existence of a capillary surface with prescribed contact angle,, \emph{Comm. Pure Appl. Math.}, 28 (1975), 189.
|
[14] |
N. S. Trudinger, The Dirichlet problem for the prescribed curvature equations,, \emph{Arch. Rational Mech. Anal.}, 111 (1990), 153.
doi: 10.1007/BF00375406. |
[15] |
N. N. Ural'tseva, The solvability of the capillary problem,, \emph{(Russian) Vestnik Leningrad. Univ. No. 19 Mat. Meh. Astronom.Vyp.}, 4 (1973), 54.
|
[16] |
X. J. Wang, Interior gradient estimates for mean curvature equations,, \emph{Math.Z.}, 228 (1998), 73.
doi: 10.1007/PL00004604. |
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