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Sc-smoothness, retractions and new models for smooth spaces
A structural condition for microscopic convexity principle
1. | Department of mathematics, Tongji University, Shanghai 200092, China |
2. | Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6, Canada |
[1] |
Chuanqiang Chen. On the microscopic spacetime convexity principle for fully nonlinear parabolic equations II: Spacetime quasiconcave solutions. Discrete and Continuous Dynamical Systems, 2016, 36 (9) : 4761-4811. doi: 10.3934/dcds.2016007 |
[2] |
Chuanqiang Chen. On the microscopic spacetime convexity principle of fully nonlinear parabolic equations I: Spacetime convex solutions. Discrete and Continuous Dynamical Systems, 2014, 34 (9) : 3383-3402. doi: 10.3934/dcds.2014.34.3383 |
[3] |
Mustapha Ait Rami, John Moore. Partial stabilizability and hidden convexity of indefinite LQ problem. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 221-239. doi: 10.3934/naco.2016009 |
[4] |
Kim Dang Phung. Carleman commutator approach in logarithmic convexity for parabolic equations. Mathematical Control and Related Fields, 2018, 8 (3&4) : 899-933. doi: 10.3934/mcrf.2018040 |
[5] |
David L. Finn. Convexity of level curves for solutions to semilinear elliptic equations. Communications on Pure and Applied Analysis, 2008, 7 (6) : 1335-1343. doi: 10.3934/cpaa.2008.7.1335 |
[6] |
Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395 |
[7] |
Qing Liu, Atsushi Nakayasu. Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces. Discrete and Continuous Dynamical Systems, 2019, 39 (1) : 157-183. doi: 10.3934/dcds.2019007 |
[8] |
Juan Carlos Marrero, David Martín de Diego, Eduardo Martínez. Local convexity for second order differential equations on a Lie algebroid. Journal of Geometric Mechanics, 2021, 13 (3) : 477-499. doi: 10.3934/jgm.2021021 |
[9] |
Gábor Székelyhidi, Ben Weinkove. On a constant rank theorem for nonlinear elliptic PDEs. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6523-6532. doi: 10.3934/dcds.2016081 |
[10] |
Christopher Goodrich, Carlos Lizama. Positivity, monotonicity, and convexity for convolution operators. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 4961-4983. doi: 10.3934/dcds.2020207 |
[11] |
Arrigo Cellina, Carlo Mariconda, Giulia Treu. Comparison results without strict convexity. Discrete and Continuous Dynamical Systems - B, 2009, 11 (1) : 57-65. doi: 10.3934/dcdsb.2009.11.57 |
[12] |
Eugenio Montefusco, Benedetta Pellacci, Marco Squassina. Energy convexity estimates for non-degenerate ground states of nonlinear 1D Schrödinger systems. Communications on Pure and Applied Analysis, 2010, 9 (4) : 867-884. doi: 10.3934/cpaa.2010.9.867 |
[13] |
Victor Isakov. On increasing stability of the continuation for elliptic equations of second order without (pseudo)convexity assumptions. Inverse Problems and Imaging, 2019, 13 (5) : 983-1006. doi: 10.3934/ipi.2019044 |
[14] |
Victor Isakov, Shuai Lu. Inverse source problems without (pseudo) convexity assumptions. Inverse Problems and Imaging, 2018, 12 (4) : 955-970. doi: 10.3934/ipi.2018040 |
[15] |
Chadi Nour, Ron J. Stern, Jean Takche. Generalized exterior sphere conditions and $\varphi$-convexity. Discrete and Continuous Dynamical Systems, 2011, 29 (2) : 615-622. doi: 10.3934/dcds.2011.29.615 |
[16] |
Antonio Greco, Antonio Iannizzotto. Existence and convexity of solutions of the fractional heat equation. Communications on Pure and Applied Analysis, 2017, 16 (6) : 2201-2226. doi: 10.3934/cpaa.2017109 |
[17] |
Petri Juutinen. Convexity of solutions to boundary blow-up problems. Communications on Pure and Applied Analysis, 2013, 12 (5) : 2267-2275. doi: 10.3934/cpaa.2013.12.2267 |
[18] |
Liran Rotem. Banach limit in convexity and geometric means for convex bodies. Electronic Research Announcements, 2016, 23: 41-51. doi: 10.3934/era.2016.23.005 |
[19] |
Kazuhiro Ishige, Paolo Salani. On a new kind of convexity for solutions of parabolic problems. Discrete and Continuous Dynamical Systems - S, 2011, 4 (4) : 851-864. doi: 10.3934/dcdss.2011.4.851 |
[20] |
Martin Gugat, Rüdiger Schultz, Michael Schuster. Convexity and starshapedness of feasible sets in stationary flow networks. Networks and Heterogeneous Media, 2020, 15 (2) : 171-195. doi: 10.3934/nhm.2020008 |
2021 Impact Factor: 1.588
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