${H}^{\infty }$ functional calculus for an elliptic operator on a half-space with general boundary conditions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 3, pp. 487-543.

Let $A$ be the ${L}^{p}$ realization ($1) of a differential operator $P\left({D}_{x},{D}_{t}\right)$ on ${ℝ}^{n}×{ℝ}^{+}$ with general boundary conditions ${B}_{k}\left({D}_{x},{D}_{t}\right)u\left(x,0\right)=0$ ($1\le k\le m$). 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 ${m}_{k}<2m$; 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.

Classification : 47A60,  35J40,  47F05
@article{ASNSP_2002_5_1_3_487_0,
author = {Dore, Giovanni and Venni, Alberto},
title = {$H^\infty$ functional calculus for an elliptic operator on a half-space with general boundary conditions},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {487--543},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {3},
year = {2002},
zbl = {1072.47014},
mrnumber = {1990671},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2002_5_1_3_487_0/}
}
Dore, Giovanni; 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, Série 5, Tome 1 (2002) no. 3, pp. 487-543. http://www.numdam.org/item/ASNSP_2002_5_1_3_487_0/

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