Unique continuation for sublinear elliptic equations based on Carleman estimates
In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong unique continuation property. Moreover, we also discuss the uniq...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
20 July 2018
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| In: |
Journal of differential equations
Year: 2018, Volume: 265, Issue: 11, Pages: 6009-6035 |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2018.07.025 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jde.2018.07.025 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022039618303899 
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| Author Notes: | Angkana Rüland |
MARC
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| 520 | |a In this article we deal with different forms of the unique continuation property for second order elliptic equations with nonlinear potentials of sublinear growth. Under suitable regularity assumptions, we prove the weak and the strong unique continuation property. Moreover, we also discuss the unique continuation property from measurable sets, which shows that nodal domains to these equations must have vanishing Lebesgue measure. Our methods rely on suitable Carleman estimates, for which we include the sublinear potential into the main part of the operator. | ||
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| 650 | 4 | |a Unique continuation | |
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