Abstract
Existence, uniqueness (even stability), and regularity are established for a special system of variational inequalities of obstacle type. The system is only considered to be elliptic in the weakest possible sense. The system includes a version of the biharmonic and polyharmonic obstacle problems. The main aspect of this problem and the approach here is its reduction via algebraic invarients to special canonical forms. One might view this work as the beginnings of a “group analysis” of variational inequalities.
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This paper is dedicated to the memory of Guido Stampacchia (1922–1978).
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Adams, D.R. Weakly elliptic systems with obstacle constraints Part II — An N × N model problem. J Geom Anal 10, 379–416 (2000). https://doi.org/10.1007/BF02921942
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DOI: https://doi.org/10.1007/BF02921942