Boundary value problems for degenerate elliptic-parabolic equations of the fourth order

Author:
Robert G. Root

Journal:
Trans. Amer. Math. Soc. **324** (1991), 109-134

MSC:
Primary 35M10; Secondary 35D05, 35J70

DOI:
https://doi.org/10.1090/S0002-9947-1991-0986699-9

MathSciNet review:
986699

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider boundary value problems for the fourth-order linear equation

*Sulle equazioni differenziali lineari ellitico-paraboliche del secondo ordine*, Atti Accad. Naz. Lincei Mem. (8)

**5**(1956), 1-30], because of the degeneracy, there may be characteristic portions of the boundary; however, we restrict our attention to the noncharacteristic case. We define a weak solution to the Dirichlet problem and obtain existence and uniqueness results. The question of regularity is addressed; elliptic regularization is used to obtain a Sobolev-type global regularity result. The equation models an anisotropic, inhomogeneous plate under tension that can lose stiffness at any point and in any direction. The regularity result has the satisfying physical interpretation that sufficient tension results in a smooth solution.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1991-0986699-9

Keywords:
Elliptic-parabolic,
degenerate elliptic,
4th order higher order,
elastic plate,
anisotropic,
inhomogeneous,
plate under tension

Article copyright:
© Copyright 1991
American Mathematical Society