On the boundary value problem of the biharmonic operator on domains with angular corners
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Publication:3889434
DOI10.1002/mma.1670020416zbMath0445.35023OpenAlexW2110176271MaRDI QIDQ3889434
Publication date: 1980
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/mma.1670020416
Asymptotic behavior of solutions to PDEs (35B40) Stress concentrations, singularities in solid mechanics (74G70) A priori estimates in context of PDEs (35B45) Partial differential equations of mathematical physics and other areas of application (35Q99)
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Cites Work
