Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule |
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| Authors: | Yousong Luo Andrew Eberhard |
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| Affiliation: | Department of Mathematics and Statistics, RMIT University, GPO Box 2476V, Melbourne, Victoria 3001, Australia |
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| Abstract: | A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the “fuzzy sum rule” of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,Du,D2u)=0 is under consideration. |
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| Keywords: | Fuzzy sum rule Non-smooth analysis Viscosity solutions Comparison principles |
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