Fractal Strichartz estimate for the wave equation

DOI10.1016/j.na.2016.11.006zbMath1355.35005arXiv1611.00206OpenAlexW2548646370MaRDI QIDQ730410

Sanghyuk Lee, Chu-Hee Cho, Seheon Ham

Publication date: 27 December 2016

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.00206

zbMATH Keywords

sharp estimategeneral measure

Mathematics Subject Classification ID

Wave equation (35L05) Initial value problems for second-order hyperbolic equations (35L15) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (8)

Pointwise convergence of sequential Schrödinger means ⋮ Fourier decay of fractal measures on surfaces of co-dimension two in \(\mathbb{R}^5\) ⋮ Fourier decay of fractal measures on hyperboloids ⋮ Dimension of divergence set of the wave equation ⋮ Improved decay of conical averages of the Fourier transform ⋮ Hausdorff dimension and projections related to intersections ⋮ Circular average relative to fractal measures ⋮ Improved bounds for restricted projection families via weighted Fourier restriction

Cites Work

• Unnamed Item
• Unnamed Item
• Bounds on oscillatory integral operators based on multilinear estimates
• Nonlinear small data scattering for the wave and Klein-Gordon equation
• The global Cauchy problem for the nonlinear Klein-Gordon equation
• On the multilinear restriction and Kakeya conjectures
• On Falconer's distance set conjecture
• Unions of hyperplanes, unions of spheres, and some related estimates
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• Hausdorff dimension and distance sets
• A sharp bilinear restriction estimate for paraboloids
• Local smoothing type estimates on \(L^p\) for large \(p\)
• Average decay of the Fourier transform of measures with applications
• A sharp bilinear cone restriction estimate
• A note on the Fourier transform of fractal measures
• On existence and scattering with minimal regularity for semilinear wave equations
• Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations
• A bilinear approach to cone multipliers. II: Applications
• Restriction estimates for space curves with respect to general measures
• Some remarks on Strichartz estimates for the homogeneous wave equation
• A restriction estimate using polynomial partitioning
• Packing spheres and fractal Strichartz estimates in $\mathbb {R}^d$ for $d\geq 3$
• Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets
• A bilinear approach to the restriction and Kakeya conjectures
• Endpoint Strichartz estimates
• Space‐time estimates for null forms and the local existence theorem
• On a Problem Related to Sphere and Circle Packing
• Bilinear restriction estimates for surfaces with curvatures of different signs

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