-
Previous Article
Hylomorphic solitons on lattices
- DCDS Home
- This Issue
-
Next Article
Preface
A Liouville theorem for solutions to the linearized Monge-Ampere equation
1. | Department of Mathematics, Columbia University, Columbia University, New York, NY 10027, United States |
$ L_$φ$ u$:$=\sum $φij$u_{ij}=0$
must be linear in $2D$. The function φ is assumed to have the Monge-Ampere measure $\det D^2 $φ bounded away from $0$ and $\infty$.
[1] |
Gregorio Díaz, Jesús Ildefonso Díaz. Parabolic Monge-Ampere equations giving rise to a free boundary: The worn stone model. Conference Publications, 2015, 2015 (special) : 369-378. doi: 10.3934/proc.2015.0369 |
[2] |
Wen Wang, Dapeng Xie, Hui Zhou. Local Aronson-Bénilan gradient estimates and Harnack inequality for the porous medium equation along Ricci flow. Communications on Pure and Applied Analysis, 2018, 17 (5) : 1957-1974. doi: 10.3934/cpaa.2018093 |
[3] |
Daniela De Silva, Ovidiu Savin. A note on higher regularity boundary Harnack inequality. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 6155-6163. doi: 10.3934/dcds.2015.35.6155 |
[4] |
Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153 |
[5] |
Giuseppe Di Fazio, Maria Stella Fanciullo, Pietro Zamboni. Harnack inequality for degenerate elliptic equations and sum operators. Communications on Pure and Applied Analysis, 2015, 14 (6) : 2363-2376. doi: 10.3934/cpaa.2015.14.2363 |
[6] |
Jinggang Tan, Jingang Xiong. A Harnack inequality for fractional Laplace equations with lower order terms. Discrete and Continuous Dynamical Systems, 2011, 31 (3) : 975-983. doi: 10.3934/dcds.2011.31.975 |
[7] |
Fen-Fen Yang. Harnack inequality and gradient estimate for functional G-SDEs with degenerate noise. Probability, Uncertainty and Quantitative Risk, , () : -. doi: 10.3934/puqr.2022008 |
[8] |
Fabio Paronetto. A Harnack type inequality and a maximum principle for an elliptic-parabolic and forward-backward parabolic De Giorgi class. Discrete and Continuous Dynamical Systems - S, 2017, 10 (4) : 853-866. doi: 10.3934/dcdss.2017043 |
[9] |
Teo Kukuljan. Higher order parabolic boundary Harnack inequality in C1 and Ck, α domains. Discrete and Continuous Dynamical Systems, 2022, 42 (6) : 2667-2698. doi: 10.3934/dcds.2021207 |
[10] |
Qi-Rui Li, Xu-Jia Wang. Regularity of the homogeneous Monge-Ampère equation. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 6069-6084. doi: 10.3934/dcds.2015.35.6069 |
[11] |
Hubert L. Bray, Marcus A. Khuri. A Jang equation approach to the Penrose inequality. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 741-766. doi: 10.3934/dcds.2010.27.741 |
[12] |
Luca Codenotti, Marta Lewicka. Visualization of the convex integration solutions to the Monge-Ampère equation. Evolution Equations and Control Theory, 2019, 8 (2) : 273-300. doi: 10.3934/eect.2019015 |
[13] |
Bo Guan, Qun Li. A Monge-Ampère type fully nonlinear equation on Hermitian manifolds. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 1991-1999. doi: 10.3934/dcdsb.2012.17.1991 |
[14] |
Alessio Figalli, Young-Heon Kim. Partial regularity of Brenier solutions of the Monge-Ampère equation. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 559-565. doi: 10.3934/dcds.2010.28.559 |
[15] |
Fatma Gamze Düzgün, Ugo Gianazza, Vincenzo Vespri. $1$-dimensional Harnack estimates. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 675-685. doi: 10.3934/dcdss.2016021 |
[16] |
Adam M. Oberman. Wide stencil finite difference schemes for the elliptic Monge-Ampère equation and functions of the eigenvalues of the Hessian. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 221-238. doi: 10.3934/dcdsb.2008.10.221 |
[17] |
Zhijun Zhang. Optimal global asymptotic behavior of the solution to a singular monge-ampère equation. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1129-1145. doi: 10.3934/cpaa.2020053 |
[18] |
Shuyu Gong, Ziwei Zhou, Jiguang Bao. Existence and uniqueness of viscosity solutions to the exterior problem of a parabolic Monge-Ampère equation. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4921-4936. doi: 10.3934/cpaa.2020218 |
[19] |
Diego Maldonado. On interior $C^2$-estimates for the Monge-Ampère equation. Discrete and Continuous Dynamical Systems, 2018, 38 (3) : 1427-1440. doi: 10.3934/dcds.2018058 |
[20] |
Haitao Yang, Yibin Chang. On the blow-up boundary solutions of the Monge -Ampére equation with singular weights. Communications on Pure and Applied Analysis, 2012, 11 (2) : 697-708. doi: 10.3934/cpaa.2012.11.697 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]