文档介绍：HARMONIC ANAL YSIS AND
P AR TIAL DIFFERENTIAL EQUA TIONS
BJ
RN E
J
D AHLBER G
CARLOS E
KENIG
ISSN
DEP AR TMENT OF MA THEMA TICS
CHALMERS UNIVERSITY OF TECHNOLOGY
AND THE UNIVERSITY OF G
G
F OREW ORD
These lecture notes are based on a course I ga v e
rst at Univ ersity of T exas
Austin
during the academic y ear
and at Univ ersity of G
in the fall of
My purp ose in those lectures w as to present some of the required background in order
to presen t the recen t results on the solv abilit y of b oundary v alue problems in domains
b oundaries
These notes concen trate on the b oundary v alue problems for the
with
bad
Laplace op erator
for plete survey of results
w e refer to the survey article b y Carlos
Kenig
I am v ery grateful for this kind p ermission to include it here
It is also m y pleasure
to ackno wledge m y gratitude to Peter Kumlin for excellen t w ork in preparing these notes
for publication
January
Bj
rn
E
J
Dahlb erg
i
ii
Con ten ts
In tro duction
Diric hlet Problem for Lipsc hitz Domain
The Setup
Pro ofs of Theorem
and Theorem
Pro of of Theorem
Pro of of Theorem
Pro of of Theorem
argumen ts for the
Diric hlet Problem for Lipsc hitz domains
The
nal
L
theory
of solutions to Diric hlet and Neumann problems for Lipsc hitz
Existence
p
domains
The optimal L
results
Index
endix
C
E
Kenig
Recen t Progress on Boundary V alue Problems on
App
Domains
Lipsc hitz
App endix
B
E
Dahlb erg
C
E
Kenig
Hardy spaces and the Neumann
p
Problem in L for Laplace
s equation in Lipsc hitz domains
iii
iv
Chapter
In tro duction
In this course w e will study b oundary v alue problems
BVP
s
for linear elliptic PDE
s
with constan t co e
cien
ts in Lipsc hitz
domains