# $$L^{p}$$ L p -theory of elliptic differential operators with unbounded coefficients

$$L^{p}$$ L p -theory of elliptic differential operators with unbounded coefficients In this paper, we consider the generation of strongly continuous analytic semigroups on $$L^p((0,\omega ),\mu _{p}\, dx)$$ L p ( ( 0 , ω ) , μ p d x ) and $$L^p((0,\omega ), dx), 1<p<\infty$$ L p ( ( 0 , ω ) , d x ) , 1 < p < ∞ , by a family of second order elliptic operators of the form [Equation not available: see fulltext.]As in [24], we shall prove the generation results on $$L^2$$ L 2 -spaces using the sesquilinear forms. More general results are obtained by using interpolation procedure and Neuberger’s theorem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Semigroup Forum Springer Journals

# $$L^{p}$$ L p -theory of elliptic differential operators with unbounded coefficients

, Volume 95 (1) – Feb 24, 2017
26 pages

/lp/springer_journal/l-p-l-p-theory-of-elliptic-differential-operators-with-unbounded-04KjKUXBYq
Publisher
Springer US
Subject
Mathematics; Algebra
ISSN
0037-1912
eISSN
1432-2137
D.O.I.
10.1007/s00233-017-9855-8
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we consider the generation of strongly continuous analytic semigroups on $$L^p((0,\omega ),\mu _{p}\, dx)$$ L p ( ( 0 , ω ) , μ p d x ) and $$L^p((0,\omega ), dx), 1<p<\infty$$ L p ( ( 0 , ω ) , d x ) , 1 < p < ∞ , by a family of second order elliptic operators of the form [Equation not available: see fulltext.]As in [24], we shall prove the generation results on $$L^2$$ L 2 -spaces using the sesquilinear forms. More general results are obtained by using interpolation procedure and Neuberger’s theorem.

### Journal

Semigroup ForumSpringer Journals

Published: Feb 24, 2017

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