Abstract
We prove the square integrability of the second derivatives of the solution of an elliptic second order equation in a general convex domain, bounded in the n-dimensional Euclidean space, under monotonic boundary conditions. Our boundary conditions are general enough to include strongly non-linear conditions as for instance Signorini's. There is no restriction concerning the singularities of the boundary of the convex domain in which the equation is considered; this domain is allowed for instance to be a two-dimensional polygon or a three-dimensional polyhedron.
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Grisvard, P. (1976). Smoothness of the solution of a monotonic boundary value problem for a second order elliptic equation in a general convex domain. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 564. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087334
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DOI: https://doi.org/10.1007/BFb0087334
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