Remarks on dispersive estimates and curvature

Previous Article
A result on Hardy-Sobolev critical elliptic equations with boundary singularities
CPAA Home
This Issue
Next Article
Periodic solutions of a periodic scalar piecewise ode

March 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

Abstract
Related Papers

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.

Keywords: Strichartz estimates, Dispersive estimates, Gaussian curvature..

Mathematics Subject Classification: Primary: 35S05; Secondary: 35B45, 47G3.

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]	Younghun Hong, Changhun Yang. Uniform Strichartz estimates on the lattice. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3239-3264. doi: 10.3934/dcds.2019134
[4]	Gong Chen. Strichartz estimates for charge transfer models. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1201-1226. doi: 10.3934/dcds.2017050
[5]	Robert Schippa. Sharp Strichartz estimates in spherical coordinates. Communications on Pure & Applied Analysis, 2017, 16 (6) : 2047-2051. doi: 10.3934/cpaa.2017100
[6]	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
[7]	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
[8]	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
[9]	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
[10]	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
[11]	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
[12]	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
[13]	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
[14]	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
[15]	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
[16]	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
[17]	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
[18]	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
[19]	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
[20]	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

2018 Impact Factor: 0.925

American Institute of Mathematical Sciences