This article is available for purchase or by subscription. See below.
Abstract
|
We consider wave equations with time-independent coefficients that have
regularity in space. We show that, for nontrivial ranges of
and
, the standard
inhomogeneous initial value problem for the wave equation is well posed in Sobolev spaces
over the
Hardy spaces
for Fourier integral operators introduced recently by the authors
and Portal, following work of Smith. In spatial dimensions
and
, this includes
the full range
.
As a corollary, we obtain the optimal fixed-time
regularity for such equations, generalizing work of Seeger, Sogge and Stein in the case
of smooth coefficients.
|
PDF Access Denied
We have not been able to recognize your IP address
3.133.116.254
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.
You may also contact us at
contact@msp.org
or by using our
contact form.
Or, you may purchase this single article for
USD 40.00:
Keywords
rough wave equations, $L^{p}$ regularity, Hardy spaces for
Fourier integral operators
|
Mathematical Subject Classification
Primary: 35R05
Secondary: 35A27, 35L05, 42B37
|
Milestones
Received: 4 October 2021
Revised: 8 June 2022
Accepted: 12 October 2022
Published: 24 August 2023
|
© 2023 MSP (Mathematical Sciences
Publishers). |
|