2007, 6(1): 203-212. doi: 10.3934/cpaa.2007.6.203

Remarks on dispersive estimates and curvature

1. 

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  March 2006 Revised  October 2006 Published  December 2006

We investigate connections between certain dispersive estimates of a (pseudo) differential operator of real principal type and the number of non-vanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.
Citation: Fabio Nicola. Remarks on dispersive estimates and curvature. Communications on Pure & Applied Analysis, 2007, 6 (1) : 203-212. doi: 10.3934/cpaa.2007.6.203
[1]

Jin-Cheng Jiang, Chengbo Wang, Xin Yu. Generalized and weighted Strichartz estimates. Communications on Pure & Applied Analysis, 2012, 11 (5) : 1723-1752. doi: 10.3934/cpaa.2012.11.1723

[2]

Robert Schippa. Generalized inhomogeneous Strichartz estimates. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3387-3410. doi: 10.3934/dcds.2017143

[3]

Gong Chen. Strichartz estimates for charge transfer models. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1201-1226. doi: 10.3934/dcds.2017050

[4]

Robert Schippa. Sharp Strichartz estimates in spherical coordinates. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2047-2051. doi: 10.3934/cpaa.2017100

[5]

Yonggeun Cho, Tohru Ozawa, Suxia Xia. Remarks on some dispersive estimates. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1121-1128. doi: 10.3934/cpaa.2011.10.1121

[6]

Delio Mugnolo. Gaussian estimates for a heat equation on a network. Networks & Heterogeneous Media, 2007, 2 (1) : 55-79. doi: 10.3934/nhm.2007.2.55

[7]

Luca Di Persio, Giacomo Ziglio. Gaussian estimates on networks with applications to optimal control. Networks & Heterogeneous Media, 2011, 6 (2) : 279-296. doi: 10.3934/nhm.2011.6.279

[8]

Chu-Hee Cho, Youngwoo Koh, Ihyeok Seo. On inhomogeneous Strichartz estimates for fractional Schrödinger equations and their applications. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 1905-1926. doi: 10.3934/dcds.2016.36.1905

[9]

Vladimir Georgiev, Atanas Stefanov, Mirko Tarulli. Smoothing-Strichartz estimates for the Schrodinger equation with small magnetic potential. Discrete & Continuous Dynamical Systems - A, 2007, 17 (4) : 771-786. doi: 10.3934/dcds.2007.17.771

[10]

Youngwoo Koh, Ihyeok Seo. Strichartz estimates for Schrödinger equations in weighted $L^2$ spaces and their applications. Discrete & Continuous Dynamical Systems - A, 2017, 37 (9) : 4877-4906. doi: 10.3934/dcds.2017210

[11]

Younghun Hong. Strichartz estimates for $N$-body Schrödinger operators with small potential interactions. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5355-5365. doi: 10.3934/dcds.2017233

[12]

Michael Goldberg. Strichartz estimates for Schrödinger operators with a non-smooth magnetic potential. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 109-118. doi: 10.3934/dcds.2011.31.109

[13]

René Henrion. Gradient estimates for Gaussian distribution functions: application to probabilistically constrained optimization problems. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 655-668. doi: 10.3934/naco.2012.2.655

[14]

Jeremy L. Marzuola. Dispersive estimates using scattering theory for matrix Hamiltonian equations. Discrete & Continuous Dynamical Systems - A, 2011, 30 (4) : 995-1035. doi: 10.3934/dcds.2011.30.995

[15]

Michael Ruzhansky, Jens Wirth. Dispersive type estimates for fourier integrals and applications to hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 1263-1270. doi: 10.3934/proc.2011.2011.1263

[16]

M. Burak Erdoǧan, William R. Green. Dispersive estimates for matrix Schrödinger operators in dimension two. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4473-4495. doi: 10.3934/dcds.2013.33.4473

[17]

Haruya Mizutani. Strichartz estimates for Schrödinger equations with variable coefficients and unbounded potentials II. Superquadratic potentials. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2177-2210. doi: 10.3934/cpaa.2014.13.2177

[18]

Sun-Yung Alice Chang, Xi-Nan Ma, Paul Yang. Principal curvature estimates for the convex level sets of semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1151-1164. doi: 10.3934/dcds.2010.28.1151

[19]

Jinju Xu. A new proof of gradient estimates for mean curvature equations with oblique boundary conditions. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1719-1742. doi: 10.3934/cpaa.2016010

[20]

Xi-Nan Ma, Jiang Ye, Yun-Hua Ye. Principal curvature estimates for the level sets of harmonic functions and minimal graphs in $R^3$. Communications on Pure & Applied Analysis, 2011, 10 (1) : 225-243. doi: 10.3934/cpaa.2011.10.225

2016 Impact Factor: 0.801

Metrics

  • PDF downloads (2)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]