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The Kato Square Root Problem for Mixed Boundary Value Problems
Author(s) -
Axelsson Andreas,
Keith Stephen,
McIntosh Alan
Publication year - 2006
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610706022873
Subject(s) - lipschitz continuity , mathematics , square root , divergence (linguistics) , quadratic equation , lipschitz domain , boundary value problem , square (algebra) , boundary (topology) , pure mathematics , order (exchange) , root (linguistics) , mathematical analysis , geometry , philosophy , linguistics , finance , economics
We solve the Kato square root problem for second order elliptic systems in divergence form under mixed boundary conditions on Lipschitz domains. This answers a question posed by Lions in 1962. To do this we develop a general theory of quadratic estimates and functional calculi for complex perturbations of Dirac‐type operators on Lipschitz domains.