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Equilibrium points of a singular cooperative system with free boundary
In this paper we initiate the study of maps minimising the energy∫D(|∇u|2+2|u|)dx, which, due to Lipschitz character of the integrand, gives rise to the singular Euler equationsΔu=u|u|χ{|u|>0},u=(u1,⋯,um). Our primary goal in this paper is to set up a road map for future developments of the theor...
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Published in: | Advances in mathematics (New York. 1965) 2015-08, Vol.280, p.743-771 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | In this paper we initiate the study of maps minimising the energy∫D(|∇u|2+2|u|)dx, which, due to Lipschitz character of the integrand, gives rise to the singular Euler equationsΔu=u|u|χ{|u|>0},u=(u1,⋯,um). Our primary goal in this paper is to set up a road map for future developments of the theory related to such energy minimising maps.
Our results here concern regularity of the solution as well as that of the free boundary. They are achieved by using monotonicity formulas and epiperimetric inequalities, in combination with geometric analysis. |
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ISSN: | 0001-8708 1090-2082 1090-2082 |
DOI: | 10.1016/j.aim.2015.04.014 |