Implicit elliptic differential equations |
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Authors: | Salvatore A Marano |
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Institution: | (1) Department of Mathematics, University of Catania, Viale A. Doria 6, 95125 Catania, Italy |
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Abstract: | Let be a bounded domain in
n
(n 3) having a smooth boundary, letY be a closed, connected and locally connected subset of
h
, letf be a real-valued function defined on ×
h
×
nh
×Y, and letL be a linear, second-order elliptic operator. In this paper, the existence of strong solutionsu W
2,p
(,
h
) W
0
1,p
(,
h
) (n<p<+) to the implicit elliptic equationf(x, u, Du, Lu)=0, whereu=(u
1,u
2, ...,u
h
),Du=(Du
1,Du
2, ...,Du
h
) andLu=(Lu
1,Lu
2, ...,Lu
h
), is established. The abstract framework where the equation is studied is that of set-valued analysis.Dedicated to Professor G. Pulvirenti on the occasion of his sixtieth birthday |
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Keywords: | Implicit elliptic equations elliptic differential inclusions strong solutions |
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