Continuous dependence on obstacles for the double obstacle problem on metric spaces |
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Authors: | Zohra Farnana |
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Affiliation: | Department of Mathematics, Linköpings universitet, SE-581 83 Linköping, Sweden |
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Abstract: | Let X be a complete metric space equipped with a doubling Borel measure supporting a p-Poincaré inequality. We obtain various convergence results for solutions of double obstacle problems on open subsets of X. In particular, we consider a sequence of double obstacle problems with converging obstacles and show that the corresponding solutions converge as well. We use the convergence properties to define and study a generalized solution of the double obstacle problem. |
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Keywords: | primary, 49J40 secondary, 31C45 |
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