-
Previous Article
Long time behavior of solutions to a Schrödinger-Poisson system in $R^3$
- CPAA Home
- This Issue
-
Next Article
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, Acta Math., 155 (1985), 261-301.
doi: 10.1007/BF02392544. |
[2] |
C. Gerhardt, Global regularity of the solutions to the capillary problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 3 (1976), 157-175. |
[3] |
P. F. Guan and X. N. Ma, The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equations, Invent. Math., 151 (2003), 553-577.
doi: 10.1007/s00222-002-0259-2. |
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag Berlin, 2001,xiv+517 pp. |
[5] |
N. J. Korevaar, Maximum principle gradient estimates for the capillary problem, Comm. in Partial Differential Equations, 13 (1988), 1-31.
doi: 10.1080/03605308808820536. |
[6] |
G. M. Lieberman, The conormal derivative problem for elliptic equations of variational type, J.Differential Equations, 49 (1983), 218-257.
doi: 10.1016/0022-0396(83)90013-X. |
[7] |
G. M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations, Nonlinear Analysis. Theory. Method $ & $ Applications, 8 (1984), 49-65.
doi: 10.1016/0362-546X(84)90027-0. |
[8] |
G. M. Lieberman, Gradient bounds for solutions of nonuniformly elliptic oblique derivative problems, Nonlinear Anal., 11 (1987), 49-61.
doi: 10.1016/0362-546X(87)90025-3. |
[9] |
G. M. Lieberman, Gradient estimates for capillary-type problems via the maximum principle, Commun. in Partial Differential Equations, 13 (1988), 33-59.
doi: 10.1080/03605308808820537. |
[10] |
G. M. Lieberman, Oblique Boundary Value Problems for Elliptic Equations, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. xvi+509 pp.
doi: 10.1142/8679. |
[11] |
X. N. Ma and J. J. Xu, Gradient estimates of mean curvature equations with Neumann boundary condition, Advances in Mathematics, 290 (2016), 1010-1039.
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, Arch. Rational Mech. Anal., 61 (1976), 19-34. |
[13] |
J. Spruck, On the existence of a capillary surface with prescribed contact angle, Comm. Pure Appl. Math., 28 (1975), 189-200. |
[14] |
N. S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rational Mech. Anal., 111 (1990), 153-179.
doi: 10.1007/BF00375406. |
[15] |
N. N. Ural'tseva, The solvability of the capillary problem, (Russian) Vestnik Leningrad. Univ. No. 19 Mat. Meh. Astronom.Vyp., 4 (1973), 54-64. |
[16] |
X. J. Wang, Interior gradient estimates for mean curvature equations, Math.Z., 228 (1998), 73-81.
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, Acta Math., 155 (1985), 261-301.
doi: 10.1007/BF02392544. |
[2] |
C. Gerhardt, Global regularity of the solutions to the capillary problem, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 3 (1976), 157-175. |
[3] |
P. F. Guan and X. N. Ma, The Christoffel-Minkowski problem I: Convexity of solutions of a Hessian equations, Invent. Math., 151 (2003), 553-577.
doi: 10.1007/s00222-002-0259-2. |
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer-Verlag Berlin, 2001,xiv+517 pp. |
[5] |
N. J. Korevaar, Maximum principle gradient estimates for the capillary problem, Comm. in Partial Differential Equations, 13 (1988), 1-31.
doi: 10.1080/03605308808820536. |
[6] |
G. M. Lieberman, The conormal derivative problem for elliptic equations of variational type, J.Differential Equations, 49 (1983), 218-257.
doi: 10.1016/0022-0396(83)90013-X. |
[7] |
G. M. Lieberman, The nonlinear oblique derivative problem for quasilinear elliptic equations, Nonlinear Analysis. Theory. Method $ & $ Applications, 8 (1984), 49-65.
doi: 10.1016/0362-546X(84)90027-0. |
[8] |
G. M. Lieberman, Gradient bounds for solutions of nonuniformly elliptic oblique derivative problems, Nonlinear Anal., 11 (1987), 49-61.
doi: 10.1016/0362-546X(87)90025-3. |
[9] |
G. M. Lieberman, Gradient estimates for capillary-type problems via the maximum principle, Commun. in Partial Differential Equations, 13 (1988), 33-59.
doi: 10.1080/03605308808820537. |
[10] |
G. M. Lieberman, Oblique Boundary Value Problems for Elliptic Equations, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. xvi+509 pp.
doi: 10.1142/8679. |
[11] |
X. N. Ma and J. J. Xu, Gradient estimates of mean curvature equations with Neumann boundary condition, Advances in Mathematics, 290 (2016), 1010-1039.
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, Arch. Rational Mech. Anal., 61 (1976), 19-34. |
[13] |
J. Spruck, On the existence of a capillary surface with prescribed contact angle, Comm. Pure Appl. Math., 28 (1975), 189-200. |
[14] |
N. S. Trudinger, The Dirichlet problem for the prescribed curvature equations, Arch. Rational Mech. Anal., 111 (1990), 153-179.
doi: 10.1007/BF00375406. |
[15] |
N. N. Ural'tseva, The solvability of the capillary problem, (Russian) Vestnik Leningrad. Univ. No. 19 Mat. Meh. Astronom.Vyp., 4 (1973), 54-64. |
[16] |
X. J. Wang, Interior gradient estimates for mean curvature equations, Math.Z., 228 (1998), 73-81.
doi: 10.1007/PL00004604. |
[1] |
Carlo Orrieri. A stochastic maximum principle with dissipativity conditions. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5499-5519. doi: 10.3934/dcds.2015.35.5499 |
[2] |
Alberto Boscaggin, Francesca Colasuonno, Benedetta Noris. Positive radial solutions for the Minkowski-curvature equation with Neumann boundary conditions. Discrete and Continuous Dynamical Systems - S, 2020, 13 (7) : 1921-1933. doi: 10.3934/dcdss.2020150 |
[3] |
Zhengchao Ji. Cylindrical estimates for mean curvature flow in hyperbolic spaces. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1199-1211. doi: 10.3934/cpaa.2021016 |
[4] |
Tae Gab Ha. Global existence and general decay estimates for the viscoelastic equation with acoustic boundary conditions. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6899-6919. doi: 10.3934/dcds.2016100 |
[5] |
Maria Francesca Betta, Rosaria Di Nardo, Anna Mercaldo, Adamaria Perrotta. Gradient estimates and comparison principle for some nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2015, 14 (3) : 897-922. doi: 10.3934/cpaa.2015.14.897 |
[6] |
Dejian Chang, Zhen Wu. Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance. Journal of Industrial and Management Optimization, 2015, 11 (1) : 27-40. doi: 10.3934/jimo.2015.11.27 |
[7] |
Ha Tuan Dung, Nguyen Thac Dung, Jiayong Wu. Sharp gradient estimates on weighted manifolds with compact boundary. Communications on Pure and Applied Analysis, 2021, 20 (12) : 4127-4138. doi: 10.3934/cpaa.2021148 |
[8] |
Hancheng Guo, Jie Xiong. A second-order stochastic maximum principle for generalized mean-field singular control problem. Mathematical Control and Related Fields, 2018, 8 (2) : 451-473. doi: 10.3934/mcrf.2018018 |
[9] |
Tian Chen, Zhen Wu. A general maximum principle for partially observed mean-field stochastic system with random jumps in progressive structure. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022012 |
[10] |
H. O. Fattorini. The maximum principle in infinite dimension. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 557-574. doi: 10.3934/dcds.2000.6.557 |
[11] |
Chao Zhang, Xia Zhang, Shulin Zhou. Gradient estimates for the strong $p(x)$-Laplace equation. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 4109-4129. doi: 10.3934/dcds.2017175 |
[12] |
Xinqun Mei, Jundong Zhou. The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1187-1198. doi: 10.3934/cpaa.2021012 |
[13] |
Diego Castellaneta, Alberto Farina, Enrico Valdinoci. A pointwise gradient estimate for solutions of singular and degenerate pde's in possibly unbounded domains with nonnegative mean curvature. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1983-2003. doi: 10.3934/cpaa.2012.11.1983 |
[14] |
Zixiao Liu, Jiguang Bao. Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022081 |
[15] |
Dimitra Antonopoulou, Georgia Karali. A nonlinear partial differential equation for the volume preserving mean curvature flow. Networks and Heterogeneous Media, 2013, 8 (1) : 9-22. doi: 10.3934/nhm.2013.8.9 |
[16] |
Chiara Corsato, Franco Obersnel, Pierpaolo Omari, Sabrina Rivetti. On the lower and upper solution method for the prescribed mean curvature equation in Minkowski space. Conference Publications, 2013, 2013 (special) : 159-169. doi: 10.3934/proc.2013.2013.159 |
[17] |
Chiara Corsato, Colette De Coster, Pierpaolo Omari. Radially symmetric solutions of an anisotropic mean curvature equation modeling the corneal shape. Conference Publications, 2015, 2015 (special) : 297-303. doi: 10.3934/proc.2015.0297 |
[18] |
Elias M. Guio, Ricardo Sa Earp. Existence and non-existence for a mean curvature equation in hyperbolic space. Communications on Pure and Applied Analysis, 2005, 4 (3) : 549-568. doi: 10.3934/cpaa.2005.4.549 |
[19] |
Adel Chala, Dahbia Hafayed. On stochastic maximum principle for risk-sensitive of fully coupled forward-backward stochastic control of mean-field type with application. Evolution Equations and Control Theory, 2020, 9 (3) : 817-843. doi: 10.3934/eect.2020035 |
[20] |
Eun Heui Kim. Boundary gradient estimates for subsonic solutions of compressible transonic potential flows. Conference Publications, 2007, 2007 (Special) : 573-579. doi: 10.3934/proc.2007.2007.573 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]