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Some Dirichlet problems with bad coercivity
Topics in regularity and qualitative properties of solutions of nonlinear elliptic equations
| 1. | Departament de Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Av. Diagonal 647. 08028 Barcelona, Spain |
The first topic is the maximum principle for the operator $L$, and its applications to the moving planes method and to symmetry properties of positive solutions of semilinear problems. The second topic is a short introduction to the regularity theory for solutions of fully nonlinear elliptic equations. We prove a $C^{1,\alpha}$ estimate for classical solutions, we introduce the notion of viscosity solution, and we study Jensen’s approximate solutions.
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Wenmin Sun, Jiguang Bao. New maximum principles for fully nonlinear ODEs of second order. Discrete and Continuous Dynamical Systems, 2007, 19 (4) : 813-823. doi: 10.3934/dcds.2007.19.813 |
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Agnid Banerjee. A note on the unique continuation property for fully nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2015, 14 (2) : 623-626. doi: 10.3934/cpaa.2015.14.623 |
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2020 Impact Factor: 1.392
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