H ∞ functional calculus for an elliptic operator on a half-space with general boundary conditions

Giovanni Dore; Alberto Venni

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 3, page 487-543
  • ISSN: 0391-173X

Abstract

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Let A be the L p realization ( 1 < p < ∞ ) of a differential operator P ( D x , D t ) on ℝ n × ℝ + with general boundary conditions B k ( D x , D t ) u ( x , 0 ) = 0 ( 1 ≤ k ≤ m ). Here P is a homogeneous polynomial of order 2 m in n + 1 complex variables that satisfies a suitable ellipticity condition, and for 1 ≤ k ≤ m B k is a homogeneous polynomial of order m k < 2 m ; it is assumed that the usual complementing condition is satisfied. We prove that A is a sectorial operator with a bounded H ∞ functional calculus.

How to cite

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Dore, Giovanni, and Venni, Alberto. "$H^\infty $ functional calculus for an elliptic operator on a half-space with general boundary conditions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.3 (2002): 487-543. <http://eudml.org/doc/84479>.

@article{Dore2002,
abstract = {Let $A$ be the $L^p$ realization ($1&lt;p&lt;\infty $) of a differential operator $P(D_x,D_t)$ on $\mathbb \{R\}^n\times \mathbb \{R\}^+$ with general boundary conditions $B_k(D_x,D_t)u(x,0)=0$ ($1\le k\le m$). Here $P$ is a homogeneous polynomial of order $2m$ in $n+1$ complex variables that satisfies a suitable ellipticity condition, and for $1\le k\le m$$B_k$ is a homogeneous polynomial of order $m_k&lt;2m$; it is assumed that the usual complementing condition is satisfied. We prove that $A$ is a sectorial operator with a bounded $H^\infty $ functional calculus.},
author = {Dore, Giovanni, Venni, Alberto},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {-maximal regularity; Cauchy problem; elliptic differential operator with constant coefficients},
language = {eng},
number = {3},
pages = {487-543},
publisher = {Scuola normale superiore},
title = {$H^\infty $ functional calculus for an elliptic operator on a half-space with general boundary conditions},
url = {http://eudml.org/doc/84479},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Dore, Giovanni
AU - Venni, Alberto
TI - $H^\infty $ functional calculus for an elliptic operator on a half-space with general boundary conditions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 3
SP - 487
EP - 543
AB - Let $A$ be the $L^p$ realization ($1&lt;p&lt;\infty $) of a differential operator $P(D_x,D_t)$ on $\mathbb {R}^n\times \mathbb {R}^+$ with general boundary conditions $B_k(D_x,D_t)u(x,0)=0$ ($1\le k\le m$). Here $P$ is a homogeneous polynomial of order $2m$ in $n+1$ complex variables that satisfies a suitable ellipticity condition, and for $1\le k\le m$$B_k$ is a homogeneous polynomial of order $m_k&lt;2m$; it is assumed that the usual complementing condition is satisfied. We prove that $A$ is a sectorial operator with a bounded $H^\infty $ functional calculus.
LA - eng
KW - -maximal regularity; Cauchy problem; elliptic differential operator with constant coefficients
UR - http://eudml.org/doc/84479
ER -

References

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