On the solvability of a variational inequality problem and application to a problem of two membranes
The purpose of this work is to give a continuous convex function, for which we can characterize the subdifferential, in order to reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, w...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201004823 |
| Summary: | The purpose of this work is to give a continuous convex function,
for which we can characterize the subdifferential, in order to
reformulate a variational inequality problem: find u=(u1,u2)∈K such that for all v=(v1,v2)∈K, ∫Ω∇u1∇(v1−u1)+∫Ω∇u2∇(v2−u2)+(f,v−u)≥0 as a system of independent equations, where f belongs to L2(Ω)×L2(Ω) and K={v∈H01(Ω)×H01(Ω):v1≥v2 a.e. in Ω}. |
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| ISSN: | 0161-1712 1687-0425 |