Singular Solutions of Fully Nonlinear Elliptic Equations and Applications |
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Authors: | Scott N. Armstrong Boyan Sirakov Charles K. Smart |
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Affiliation: | 1. Department of Mathematics, The University of Chicago, Chicago, IL, 60637, USA 2. UFR SEGMI, Universit?? Paris 10, 92001, Nanterre Cedex, France 3. CAMS, EHESS, 54 bd Raspail, 75270, Paris Cedex 06, France 4. Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, USA
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Abstract: | We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of , and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragmén–Lindel?f result as well as a principle of positive singularities in certain Lipschitz domains. |
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