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Strongly elliptic problems near cuspidal points and edges. (English) Zbl 0853.35018
Cea, Jean (ed.) et al., Partial differential equations and functional analysis. In memory of Pierre Grisvard. Proceedings of a conference held in November 1994. Boston, MA: Birkhäuser. Prog. Nonlinear Differ. Equ. Appl. 22, 93-110 (1996).
Summary: After an overview of the various geometrical situations occurring for two-dimensional piecewise smooth domains, we concentrate on the case of outgoing cusp points. We recall results by P. Grisvard and V. G. Mazya and B. A. Plamenevskii. Then, relying on a work by J.-L. Steux, we state a result of regularity in the space of infinitely smooth functions: if the data are $$C^\infty$$, the solution is also $$C^\infty$$. We extend this result to the situation of cuspidal edges (for example the domain exterior to a cylinder lying on a plane, or two tangent tori).
For the entire collection see [Zbl 0840.00032].

##### MSC:
 35B65 Smoothness and regularity of solutions to PDEs 35J40 Boundary value problems for higher-order elliptic equations
##### Keywords:
piecewise smooth domains