An improved bilinear restriction estimate for the paraboloid in $$\mathbb {R}^3$$

نویسندگان

چکیده

Abstract We obtain a sharp bilinear restriction estimate for the paraboloid in $$\mathbb {R}^3$$ R 3 $$q>13/4.$$ q > 13 / 4 .

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Sharp Bilinear Restriction Estimate for Paraboloids

X iv :m at h/ 02 10 08 4v 2 [ m at h. C A ] 1 3 D ec 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon ...

متن کامل

An Improved Bilinear Estimate for Benjamin-ono Type Equations

A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem ut − |D| αux + uux = 0 in (−T, T ) × R u(0) = u0 is proved, for 1 < α < 2. As a consequence, local well-posedness in H(R) ∩ Ḣ(R) follows for s > − 3 4 (α − 1) and ω = 1/α − 1/2 This extends to global well-posedness for all s ≥ 0.

متن کامل

A sharp bilinear cone restriction estimate

The purpose of this paper is to prove an essentially sharp L2 Fourier restriction estimate for light cones, of the type which is called bilinear in the recent literature. Fix d ≥ 3, denote variables in Rd by (x, xd) with x ∈ Rd−1, and let Γ = {x : xd = |x| and 1 ≤ xd ≤ 2}. Let Γ1 and Γ2 be disjoint conical subsets, i.e. Γi = {x ∈ Γ : x xd ∈ Ωi} where Ωi are disjoint closed subsets of the sphere...

متن کامل

A Sharp Bilinear Restriction Estimate for Elliptic Surfaces

X iv :m at h/ 02 10 08 4v 1 [ m at h. C A ] 7 O ct 2 00 2 Abstract. Recently Wolff [28] obtained a sharp L2 bilinear restriction theorem for bounded subsets of the cone in general dimension. Here we adapt the argument of Wolff to also handle subsets of “elliptic surfaces” such as paraboloids. Except for an endpoint, this answers a conjecture of Machedon and Klainerman, and also improves upon th...

متن کامل

A Trilinear Restriction Problem for the Paraboloid in R

We establish a sharp trilinear inequality for the extension operator associated to the paraboloid in R3. Our proof relies on a recent generalisation of the classical Loomis–Whitney inequality.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Mathematische Zeitschrift

سال: 2023

ISSN: ['1432-1823', '0025-5874']

DOI: https://doi.org/10.1007/s00209-023-03237-2