-
Previous Article
Global well-posedness and scattering for Skyrme wave maps
- CPAA Home
- This Issue
-
Next Article
Local maximum principle for $L^p$-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients
On the characteristic curvature operator
1. | Department of Mathematics, Rutgers University, Hill Center for the Mathematical Sciences, 110 Frelinghuysen Rd., Piscataway 08854-8019 NJ, United States |
References:
[1] |
E. Bedford and B. Gaveau, Hypersurfaces with bounded Levi form, Indiana University Journal, 27 (1978), 867-873.
doi: 10.1512/iumj.1978.27.27058. |
[2] |
A. Bogges, "CR Manifolds and the Tangential Cauchy-Riemann Complex," Studies in Advanced Mathematics, 1991. |
[3] |
M. G. Crandall, H. Ishii and P. L. Lions, User's guide to viscosity solutions of second order Partial differential equations, Bull. Amer. Soc., 27 (1992), 1-67. |
[4] |
F. Da Lio and A. Montanari, Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature, Ann. Inst. H. Poincaré Anal. Non Linéaire, 23 (2006), 1-28. |
[5] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," second edition, Springer-Verlag, 1983. |
[6] |
H. Hofer and E. Zehnder, "Symplectic Invariants and Hamiltonian Dynamics," Birkhäuser Verlag, Basel, 1994 |
[7] |
J. G. Hounie and E. Lanconelli, An Alexander type theorem for Reinhardt domains of $\mathbb{C}^2$. Recent progress on some problems in several complex variables and partial differential equations, Contemp. Math., Amer. Math. Soc., Providence, RI, 400 (2006), 129-146. |
[8] |
J. G. Hounie and E. Lanconelli, A sphere theorem for a class of Reinhardt domains with constant Levi curvature, Forum Mathematicum, 20 (2008), 571-586.
doi: 10.1515/FORUM.2008.029. |
[9] |
H. Ishii and P. L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations, 83 (1990), 26-78.
doi: 10.1016/0022-0396(90)90068-Z. |
[10] |
E. Lanconelli and A. Montanari, Pseudoconvex fully nonlinear partial differential operators. Strong comparison theorems, J. Differential Equations, 202 (2004), 306-331.
doi: 10.1016/j.jde.2004.03.017. |
[11] |
V. Martino, A symmetry result on Reinhardt domains, Differential and Integral Equations, 24 (2011), 495-504. |
[12] |
V. Martino and A. Montanari, Graphs with prescribed the trace of the Levi form, Ann. Univ. Ferrara Sez. VII Sci. Mat., 52 (2006), 371-382.
doi: 10.1007/s11565-006-0027-0. |
[13] |
Z. Slodkowski and G. Tomassini, Weak solutions for the Levi equation and envelope of holomorphy, J. Funct. Anal., 101 (1991), 392-407.
doi: 10.1016/0022-1236(91)90164-Z. |
[14] |
Z. Slodkowski, G. Tomassini, The Levi equation in higher dimensions and relationships to the envelope of holomorphy, Amer. J. Math., 116 (1994), 479-499.
doi: 10.2307/2374937. |
show all references
References:
[1] |
E. Bedford and B. Gaveau, Hypersurfaces with bounded Levi form, Indiana University Journal, 27 (1978), 867-873.
doi: 10.1512/iumj.1978.27.27058. |
[2] |
A. Bogges, "CR Manifolds and the Tangential Cauchy-Riemann Complex," Studies in Advanced Mathematics, 1991. |
[3] |
M. G. Crandall, H. Ishii and P. L. Lions, User's guide to viscosity solutions of second order Partial differential equations, Bull. Amer. Soc., 27 (1992), 1-67. |
[4] |
F. Da Lio and A. Montanari, Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature, Ann. Inst. H. Poincaré Anal. Non Linéaire, 23 (2006), 1-28. |
[5] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," second edition, Springer-Verlag, 1983. |
[6] |
H. Hofer and E. Zehnder, "Symplectic Invariants and Hamiltonian Dynamics," Birkhäuser Verlag, Basel, 1994 |
[7] |
J. G. Hounie and E. Lanconelli, An Alexander type theorem for Reinhardt domains of $\mathbb{C}^2$. Recent progress on some problems in several complex variables and partial differential equations, Contemp. Math., Amer. Math. Soc., Providence, RI, 400 (2006), 129-146. |
[8] |
J. G. Hounie and E. Lanconelli, A sphere theorem for a class of Reinhardt domains with constant Levi curvature, Forum Mathematicum, 20 (2008), 571-586.
doi: 10.1515/FORUM.2008.029. |
[9] |
H. Ishii and P. L. Lions, Viscosity solutions of fully nonlinear second-order elliptic partial differential equations, J. Differential Equations, 83 (1990), 26-78.
doi: 10.1016/0022-0396(90)90068-Z. |
[10] |
E. Lanconelli and A. Montanari, Pseudoconvex fully nonlinear partial differential operators. Strong comparison theorems, J. Differential Equations, 202 (2004), 306-331.
doi: 10.1016/j.jde.2004.03.017. |
[11] |
V. Martino, A symmetry result on Reinhardt domains, Differential and Integral Equations, 24 (2011), 495-504. |
[12] |
V. Martino and A. Montanari, Graphs with prescribed the trace of the Levi form, Ann. Univ. Ferrara Sez. VII Sci. Mat., 52 (2006), 371-382.
doi: 10.1007/s11565-006-0027-0. |
[13] |
Z. Slodkowski and G. Tomassini, Weak solutions for the Levi equation and envelope of holomorphy, J. Funct. Anal., 101 (1991), 392-407.
doi: 10.1016/0022-1236(91)90164-Z. |
[14] |
Z. Slodkowski, G. Tomassini, The Levi equation in higher dimensions and relationships to the envelope of holomorphy, Amer. J. Math., 116 (1994), 479-499.
doi: 10.2307/2374937. |
[1] |
Shigeaki Koike, Andrzej Świech. Local maximum principle for $L^p$-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1897-1910. doi: 10.3934/cpaa.2012.11.1897 |
[2] |
Phuong Le, Hoang-Hung Vo. Monotonicity and symmetry of positive solutions to degenerate quasilinear elliptic systems in half-spaces and strips. Communications on Pure and Applied Analysis, 2022, 21 (3) : 1027-1048. doi: 10.3934/cpaa.2022008 |
[3] |
Rainer Buckdahn, Christian Keller, Jin Ma, Jianfeng Zhang. Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions. Probability, Uncertainty and Quantitative Risk, 2020, 5 (0) : 7-. doi: 10.1186/s41546-020-00049-8 |
[4] |
Inwon C. Kim, Helen K. Lei. Degenerate diffusion with a drift potential: A viscosity solutions approach. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 767-786. doi: 10.3934/dcds.2010.27.767 |
[5] |
Antonio Vitolo. On the growth of positive entire solutions of elliptic PDEs and their gradients. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1335-1346. doi: 10.3934/dcdss.2014.7.1335 |
[6] |
Paola Mannucci. The Dirichlet problem for fully nonlinear elliptic equations non-degenerate in a fixed direction. Communications on Pure and Applied Analysis, 2014, 13 (1) : 119-133. doi: 10.3934/cpaa.2014.13.119 |
[7] |
Ibrahim Ekren, Jianfeng Zhang. Pseudo-Markovian viscosity solutions of fully nonlinear degenerate PPDEs. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 6-. doi: 10.1186/s41546-016-0010-3 |
[8] |
Ghulamullah Saeedi, Farhad Waseel, Hadia Jalal. Existence of solutions for a class of quasilinear elliptic equations with a parameter. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022096 |
[9] |
Yuxia Guo, Jianjun Nie. Classification for positive solutions of degenerate elliptic system. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1457-1475. doi: 10.3934/dcds.2018130 |
[10] |
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure and Applied Analysis, 2021, 20 (7&8) : 2505-2518. doi: 10.3934/cpaa.2020272 |
[11] |
M. Sango. Weak solutions for a doubly degenerate quasilinear parabolic equation with random forcing. Discrete and Continuous Dynamical Systems - B, 2007, 7 (4) : 885-905. doi: 10.3934/dcdsb.2007.7.885 |
[12] |
Sachiko Ishida. $L^\infty$-decay property for quasilinear degenerate parabolic-elliptic Keller-Segel systems. Conference Publications, 2013, 2013 (special) : 335-344. doi: 10.3934/proc.2013.2013.335 |
[13] |
Yaotian Shen, Youjun Wang. Degenerate coercive quasilinear elliptic equations with subcritical or critical exponents in $ \mathbb{R}^N $. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4667-4697. doi: 10.3934/cpaa.2020197 |
[14] |
Yuya Tanaka, Tomomi Yokota. Finite-time blow-up in a quasilinear degenerate parabolic–elliptic chemotaxis system with logistic source and nonlinear production. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022075 |
[15] |
Pablo Ochoa, Julio Alejo Ruiz. A study of comparison, existence and regularity of viscosity and weak solutions for quasilinear equations in the Heisenberg group. Communications on Pure and Applied Analysis, 2019, 18 (3) : 1091-1115. doi: 10.3934/cpaa.2019053 |
[16] |
Miguel R. Nuñez-Chávez. Controllability under positive constraints for quasilinear parabolic PDEs. Mathematical Control and Related Fields, 2022, 12 (2) : 327-341. doi: 10.3934/mcrf.2021024 |
[17] |
Messoud Efendiev, Anna Zhigun. On an exponential attractor for a class of PDEs with degenerate diffusion and chemotaxis. Discrete and Continuous Dynamical Systems, 2018, 38 (2) : 651-673. doi: 10.3934/dcds.2018028 |
[18] |
Jiabao Su, Rushun Tian. Weighted Sobolev embeddings and radial solutions of inhomogeneous quasilinear elliptic equations. Communications on Pure and Applied Analysis, 2010, 9 (4) : 885-904. doi: 10.3934/cpaa.2010.9.885 |
[19] |
Antonio Ambrosetti, Zhi-Qiang Wang. Positive solutions to a class of quasilinear elliptic equations on $\mathbb R$. Discrete and Continuous Dynamical Systems, 2003, 9 (1) : 55-68. doi: 10.3934/dcds.2003.9.55 |
[20] |
Shinji Adachi, Masataka Shibata, Tatsuya Watanabe. Asymptotic behavior of positive solutions for a class of quasilinear elliptic equations with general nonlinearities. Communications on Pure and Applied Analysis, 2014, 13 (1) : 97-118. doi: 10.3934/cpaa.2014.13.97 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]