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On the Regularity of Stresses in the Closed Domain for the Linear Theory of Elasticity

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Abstract

The article deals with the estimates of the first derivatives of the solutions of the system L(u) ≡ μΔu + (λ + μ)∇(u) = −f(x). The solutions are fixed at the boundary u|∂Ω = 0. The estimates are obtained in the whole closed domain in terms of the right-hand term f in a certain “strong” norm. If the norm of f in l 2 is sufficiently small as compared to its “strong” norm, one can obtain estimates in an explicit form.

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Authors and Affiliations

  1. St. Petersburg State University, University Prospect 28, 198504, St. Petersburg, St. Peterhof

    A. I. Koshelev

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  1. A. I. Koshelev
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Koshelev, A.I. On the Regularity of Stresses in the Closed Domain for the Linear Theory of Elasticity. Journal of Mathematical Sciences 120, 1399–1406 (2004). https://doi.org/10.1023/B:JOTH.0000016056.74175.bb

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  • DOI: https://doi.org/10.1023/B:JOTH.0000016056.74175.bb

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