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Asymptotic behavior of the solution to the Poisson equation near a crack tip with nonlinear boundary conditions on the crack faces
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Russian Ac. Sci. L.
2006 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 74, no 3, 865-868 p.Article in journal (Refereed) Published
Abstract [en]

The asymptotic behavior of the solution to the Poisson equations near the crack tip with nonlinear boundary conditions and second derivatives of the in weighted Sobolev spaces were determined. The internal regularity results for the equation showed that the second derivative of u belonged to L2 in the neighborhood of interior points of the crack. The results demonstrated analogy between the properties of the solution to the linear problem and the nonlinear problem. It was also found that an asymptotic representation to the problem can be constructed near the crack tip.

Place, publisher, year, edition, pages
2006. Vol. 74, no 3, 865-868 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-37182DOI: 10.1134/S1064562406060202Local ID: 33875OAI: oai:DiVA.org:liu-37182DiVA: diva2:258031
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2017-12-13

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Kozlov, Vladimir

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