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Singular evolution on maniforlds, their smoothing properties, and soboleve inequalities
1. | CEREMADE, Université Paris Dauphine, Place de Lattre de Tassigny, F-75775 Paris Cédex 16, France |
2. | Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy |
[1] |
YanYan Li, Tonia Ricciardi. A sharp Sobolev inequality on Riemannian manifolds. Communications on Pure and Applied Analysis, 2003, 2 (1) : 1-31. doi: 10.3934/cpaa.2003.2.1 |
[2] |
Yuhua Sun. On the uniqueness of nonnegative solutions of differential inequalities with gradient terms on Riemannian manifolds. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1743-1757. doi: 10.3934/cpaa.2015.14.1743 |
[3] |
Mohamed Jleli, Bessem Samet. Nonexistence for time-fractional wave inequalities on Riemannian manifolds. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022115 |
[4] |
Patrizia Pucci, Marco Rigoli. Entire solutions of singular elliptic inequalities on complete manifolds. Discrete and Continuous Dynamical Systems, 2008, 20 (1) : 115-137. doi: 10.3934/dcds.2008.20.115 |
[5] |
Nikolaos Roidos, Yuanzhen Shao. Functional inequalities involving nonlocal operators on complete Riemannian manifolds and their applications to the fractional porous medium equation. Evolution Equations and Control Theory, 2022, 11 (3) : 793-825. doi: 10.3934/eect.2021026 |
[6] |
Mohamed Jleli, Bessem Samet. Instantaneous blow-up for nonlinear Sobolev type equations with potentials on Riemannian manifolds. Communications on Pure and Applied Analysis, 2022, 21 (6) : 2065-2078. doi: 10.3934/cpaa.2022036 |
[7] |
Jochen Merker. Generalizations of logarithmic Sobolev inequalities. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 329-338. doi: 10.3934/dcdss.2008.1.329 |
[8] |
Razvan C. Fetecau, Beril Zhang. Self-organization on Riemannian manifolds. Journal of Geometric Mechanics, 2019, 11 (3) : 397-426. doi: 10.3934/jgm.2019020 |
[9] |
Ezequiel R. Barbosa, Marcos Montenegro. On the geometric dependence of Riemannian Sobolev best constants. Communications on Pure and Applied Analysis, 2009, 8 (6) : 1759-1777. doi: 10.3934/cpaa.2009.8.1759 |
[10] |
Xiaoli Chen, Jianfu Yang. Improved Sobolev inequalities and critical problems. Communications on Pure and Applied Analysis, 2020, 19 (7) : 3673-3695. doi: 10.3934/cpaa.2020162 |
[11] |
Rossella Bartolo. Periodic orbits on Riemannian manifolds with convex boundary. Discrete and Continuous Dynamical Systems, 1997, 3 (3) : 439-450. doi: 10.3934/dcds.1997.3.439 |
[12] |
Atsushi Katsuda, Yaroslav Kurylev, Matti Lassas. Stability of boundary distance representation and reconstruction of Riemannian manifolds. Inverse Problems and Imaging, 2007, 1 (1) : 135-157. doi: 10.3934/ipi.2007.1.135 |
[13] |
David M. A. Stuart. Solitons on pseudo-Riemannian manifolds: stability and motion. Electronic Research Announcements, 2000, 6: 75-89. |
[14] |
Fei Liu, Jaume Llibre, Xiang Zhang. Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 1097-1111. doi: 10.3934/dcds.2011.29.1097 |
[15] |
Cristina Pocci. On singular limit of a nonlinear $p$-order equation related to Cahn-Hilliard and Allen-Cahn evolutions. Evolution Equations and Control Theory, 2013, 2 (3) : 517-530. doi: 10.3934/eect.2013.2.517 |
[16] |
Nakao Hayashi, Pavel I. Naumkin, Patrick-Nicolas Pipolo. Smoothing effects for some derivative nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 1999, 5 (3) : 685-695. doi: 10.3934/dcds.1999.5.685 |
[17] |
Max Fathi, Emanuel Indrei, Michel Ledoux. Quantitative logarithmic Sobolev inequalities and stability estimates. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 6835-6853. doi: 10.3934/dcds.2016097 |
[18] |
Marita Thomas. Uniform Poincaré-Sobolev and isoperimetric inequalities for classes of domains. Discrete and Continuous Dynamical Systems, 2015, 35 (6) : 2741-2761. doi: 10.3934/dcds.2015.35.2741 |
[19] |
T. V. Anoop, Nirjan Biswas, Ujjal Das. Admissible function spaces for weighted Sobolev inequalities. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3259-3297. doi: 10.3934/cpaa.2021105 |
[20] |
Maria J. Esteban. Gagliardo-Nirenberg-Sobolev inequalities on planar graphs. Communications on Pure and Applied Analysis, 2022, 21 (6) : 2101-2114. doi: 10.3934/cpaa.2022051 |
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