Variational formulas on Lipschitz domains

Elcrat, Alan R.; Miller, Kenneth G.

doi:10.1090/S0002-9947-1995-1285987-2

Variational formulas on Lipschitz domains
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by Alan R. Elcrat and Kenneth G. Miller

Trans. Amer. Math. Soc. 347 (1995), 2669-2678

DOI: https://doi.org/10.1090/S0002-9947-1995-1285987-2

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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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