Strichartz Estimates on Exterior Polygonal Domains

نویسندگان

  • DEAN BASKIN
  • JEREMY L. MARZUOLA
چکیده

Using a new local smoothing estimate of the first and third authors, we prove local-in-time Strichartz and smoothing estimates without a loss exterior to a large class of polygonal obstacles with arbitrary boundary conditions and global-in-time Strichartz estimates without a loss exterior to a large class of polygonal obstacles with Dirichlet boundary conditions. In addition, we prove a global-in-time local smoothing estimate in exterior wedge domains with Dirichlet boundary conditions and discuss some nonlinear applications.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Strichartz Estimates for the Schrödinger Equation on Polygonal Domains

We prove Strichartz estimates with a loss of derivatives for the Schrödinger equation on polygonal domains with either Dirichlet or Neumann homogeneous boundary conditions. Using a standard doubling procedure, estimates on the polygon follow from those on Euclidean surfaces with conical singularities. We develop a Littlewood-Paley squarefunction estimate with respect to the spectrum of the Lapl...

متن کامل

9 J ul 2 01 7 DECAY ESTIMATES FOR WAVE EQUATION WITH A POTENTIAL ON EXTERIOR DOMAINS

The purpose of the present paper is to establish the local energy decay estimates and dispersive estimates for 3-dimensional wave equation with a potential to the initial-boundary value problem on exterior domains. The geometrical assumptions on domains are rather general, for example non-trapping condition is not imposed in the local energy decay result. As a by-product, Strichartz estimates i...

متن کامل

Decay Estimates for Variable Coefficient Wave Equations in Exterior Domains

In this article we consider variable coefficient, time dependent wave equations in exterior domains R × (R \ Ω), n ≥ 3. We prove localized energy estimates if Ω is star-shaped, and global in time Strichartz estimates if Ω is strictly convex.

متن کامل

Global Strichartz Estimates for Nontrapping Perturbations of the Laplacian

The purpose of this paper is to establish estimates of Strichartz type, globally in space and time, for solutions to certain nontrapping, spatially compact perturbations of the Minkowski wave equation. Precisely, we consider the following wave equation on the exterior domain Ω to a compact obstacle, where the spatial dimension is an odd integer n ≥ 3.    ∂ t u(t, x)−∆gu(t, x) ...

متن کامل

Generalized Strichartz Estimates on Perturbed Wave Equation and Applications on Strauss Conjecture

The purpose of this paper is to show a general Strichartz estimate for certain perturbed wave equation under known local energy decay estimates, and as application, to get the Strauss conjecture for several convex obstacles in n = 3, 4. Our results improve on earlier work in Hidano, Metcalfe, Smith, Sogge and Zhou [14]. First, and most important, we can drop the nontrapping hypothesis and handl...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013