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Differentiability of solutions to second-order elliptic equations via dynamical systems
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
Brigham and Womens Hospital.
2011 (English)In: JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, Vol. 250, no 2, 1137-1168 p.Article in journal (Refereed) Published
Abstract [en]

For a second-order elliptic equation in divergence form we investigate conditions on the coefficients which imply that all solutions are Lipschitz continuous or differentiable at a given point. We assume the coefficients have modulus of continuity satisfying the square-Dini condition, and obtain additional conditions that examples show are sharp. Our results extend those of previous authors who assume the modulus of continuity satisfies the Dini condition. Our method involves the study of asymptotic properties of solutions to a dynamical system that is derived from the coefficients of the elliptic equation.

Place, publisher, year, edition, pages
Elsevier Science B.V., Amsterdam , 2011. Vol. 250, no 2, 1137-1168 p.
Keyword [en]
Differentiability, Weak solution, Elliptic equation, Divergence form, Modulus of continuity, Dini condition, Square-Dini condition, Dynamical system, Asymptotically constant, Uniformly stable
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-64574DOI: 10.1016/j.jde.2010.06.023ISI: 000285490300020OAI: oai:DiVA.org:liu-64574DiVA: diva2:392810
Available from: 2011-01-28 Created: 2011-01-28 Last updated: 2011-01-28

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Maz´ya, Vladimir

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