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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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Xiaoming He, Xin Zhao, Wenming Zou. Maximum principles for a fully nonlinear nonlocal equation on unbounded domains. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4387-4399. doi: 10.3934/cpaa.2020200 |
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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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Fabio Punzo. Phragmèn-Lindelöf principles for fully nonlinear elliptic equations with unbounded coefficients. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1439-1461. doi: 10.3934/cpaa.2010.9.1439 |
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Robert Jensen, Andrzej Świech. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE. Communications on Pure and Applied Analysis, 2005, 4 (1) : 199-207. doi: 10.3934/cpaa.2005.4.187 |
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Francesca Da Lio. Remarks on the strong maximum principle for viscosity solutions to fully nonlinear parabolic equations. Communications on Pure and Applied Analysis, 2004, 3 (3) : 395-415. doi: 10.3934/cpaa.2004.3.395 |
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Italo Capuzzo Dolcetta, Antonio Vitolo. Glaeser's type gradient estimates for non-negative solutions of fully nonlinear elliptic equations. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 539-557. doi: 10.3934/dcds.2010.28.539 |
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Gabrielle Nornberg, Delia Schiera, Boyan Sirakov. A priori estimates and multiplicity for systems of elliptic PDE with natural gradient growth. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3857-3881. doi: 10.3934/dcds.2020128 |
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Xavier Cabré, Manel Sanchón, Joel Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 601-609. doi: 10.3934/dcds.2016.36.601 |
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Shigeaki Koike, Andrzej Świech. Local maximum principle for $L^p$-viscosity solutions of fully nonlinear elliptic PDEs with unbounded coefficients. Communications on Pure and Applied Analysis, 2012, 11 (5) : 1897-1910. doi: 10.3934/cpaa.2012.11.1897 |
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Meng Qu, Ping Li, Liu Yang. Symmetry and monotonicity of solutions for the fully nonlinear nonlocal equation. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1337-1349. doi: 10.3934/cpaa.2020065 |
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Limei Dai. Entire solutions with asymptotic behavior of fully nonlinear uniformly elliptic equations. Communications on Pure and Applied Analysis, 2011, 10 (6) : 1707-1714. doi: 10.3934/cpaa.2011.10.1707 |
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Pierpaolo Soravia. Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Communications on Pure and Applied Analysis, 2006, 5 (1) : 213-240. doi: 10.3934/cpaa.2006.5.213 |
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Hongxia Zhang, Ying Wang. Liouville results for fully nonlinear integral elliptic equations in exterior domains. Communications on Pure and Applied Analysis, 2018, 17 (1) : 85-112. doi: 10.3934/cpaa.2018006 |
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Chunhui Qiu, Rirong Yuan. On the Dirichlet problem for fully nonlinear elliptic equations on annuli of metric cones. Discrete and Continuous Dynamical Systems, 2017, 37 (11) : 5707-5730. doi: 10.3934/dcds.2017247 |
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Lidan Wang, Lihe Wang, Chunqin Zhou. Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1241-1261. doi: 10.3934/cpaa.2021019 |
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Martino Bardi, Paola Mannucci. On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations. Communications on Pure and Applied Analysis, 2006, 5 (4) : 709-731. doi: 10.3934/cpaa.2006.5.709 |
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Antonio Vitolo, Maria E. Amendola, Giulio Galise. On the uniqueness of blow-up solutions of fully nonlinear elliptic equations. Conference Publications, 2013, 2013 (special) : 771-780. doi: 10.3934/proc.2013.2013.771 |
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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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Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch. Coupling techniques for nonlinear hyperbolic equations. Ⅱ. resonant interfaces with internal structure. Networks and Heterogeneous Media, 2021, 16 (2) : 283-315. doi: 10.3934/nhm.2021007 |
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Brian D. Ewald, Roger Témam. Maximum principles for the primitive equations of the atmosphere. Discrete and Continuous Dynamical Systems, 2001, 7 (2) : 343-362. doi: 10.3934/dcds.2001.7.343 |
2020 Impact Factor: 1.392
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