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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
AGMON Lectures on elliptic boundary value problems, Van Nostrand, New-York, 1965.
BREZIS Monotonicity methods in Hilbert space and some applications, Contributions to non linear functional analysis, Acad. Press 1971.
CHENAIS On the existence of a solution in a domain identification pro-problem, J. of Math. Anal. and Appl. Vol 52, no2, 1975.
GRISVARD Alternative de Fredholm relative au problème de Dirichlet, Bollettino della U.M.I., (4) 5, 1972.
GRISVARD Behaviour of the solutions of an elliptic boundary value problem, SYNSPADE III, Acad. Press 1975.
KADLEC La régularité de la solution du problème de Poisson, Czechoslovak Mat. J. 89, 1964.
LADYZENSKAIA-URALCEVA Equations aux dérivées partielles de type elliptique, Dunod, Paris, 1968.
LIONS Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars, Paris, 1969.
LIONS MAGENES Problèmes aux limites non homogènes tome I, Dunod, Paris, 1968.
NECAS Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0087334
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-08058-9
Online ISBN: 978-3-540-37517-3
eBook Packages: Springer Book Archive