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Transactions of the American Mathematical Society

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Variational formulas on Lipschitz domains

Authors: Alan R. Elcrat and Kenneth G. Miller
Journal: Trans. Amer. Math. Soc. 347 (1995), 2669-2678
MSC: Primary 35J20; Secondary 49Q05, 76C99, 76M30
MathSciNet review: 1285987
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Abstract: A rigorous treatment is given of variational formulas for solutions of certain Dirichlet problems for the Laplace operator on Lipschitz domains under interior variations. In particular we extend well-known variational formulas for the torsional rigidity and for capacity from the class of $ {C^1}$ domains to the class of Lipschitz domains. A motivation for this work comes from the use of variational methods in the study of Prandtl-Batchelor flows in fluid mechanics.

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