THE DIRICHLET PROBLEM FOR FULLY NONLINEAR ELLIPTIC EQUATIONS NON-DEGENERATE IN A FIXED DIRECTION

Paola Mannucci

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THE DIRICHLET PROBLEM FOR FULLY NONLINEAR ELLIPTIC EQUATIONS NON-DEGENERATE IN A FIXED DIRECTION

机译：固定方向上不退化的完全非线性椭圆型方程的Dirichlet问题

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摘要

We prove a comparison principle for viscosity solutions of a fully nonlinear equation satisfying a condition of non-degeneracy in a fixed direction. We apply these results to prove that a continuous solution of the corresponding Dirichlet problem exists. To obtain the existence of barrier functions and well-posedness, we find suitable explicit assumptions on the domain and on the ellipticity constants of the operator.

机译：我们证明了在固定方向上满足非简并性条件的完全非线性方程的粘度解的比较原理。我们应用这些结果来证明存在相应Dirichlet问题的连续解。为了获得障碍函数和适定性的存在，我们在算子的域和椭圆常数上找到合适的显式假设。

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《Communications on pure and applied analysis》 |2014年第1期|共15页
作者
Paola Mannucci;
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正文语种 eng
中图分类数学;
关键词
Viscosity solution; comparison principle; degenerate elliptic equation; Dirichlet problem; subelliptic equation; Pucci's operators; Carnot groups;

机译：粘度溶液;比较原理;退化椭圆方程;Dirichlet问题;亚椭圆方程;Pucci算子;卡诺群;

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专利

1. THE DIRICHLET PROBLEM FOR FULLY NONLINEAR ELLIPTIC EQUATIONS NON-DEGENERATE IN A FIXED DIRECTION [J] . Paola Mannucci Communications on pure and applied analysis . 2014,第1期

机译：固定方向上不退化的完全非线性椭圆型方程的Dirichlet问题
2. The Dirichlet problem for singular elliptic equations with general nonlinearities [J] . De Cicco Virginia, Giachetti Daniela, Oliva Francescantonio, Calculus of variations and partial differential equations . 2019,第4期

机译：一般非线性奇异椭圆方程的Dirichlet问题
3. THE BEHAVIOR OF SOLUTIONS TO THE DIRICHLET PROBLEM FOR SECOND ORDER ELLIPTIC EQUATIONS WITH VARIABLE NONLINEARITY EXPONENT IN A NEIGHBORHOOD OF A CONICAL BOUNDARY POINT [J] . Yu. Alkhutov, M. V. Borsuk Journal of Mathematical Sciences . 2015,第5期

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4. On the Dirichlet Problem for some Nonlinear Degenerated Elliptic Equations with Weight [C] . Mohamed El Ouaarabi, Chakir Allalou, Adil Abbassi International Conference on Optimization and Applications . 2021

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5. The Dirichlet Problem for Elliptic and Degenerate Elliptic Equations, and Related Results [D] . Le, Phi Long. 2016

机译：椭圆形和简并椭圆方程的Dirichlet问题及相关结果
6. Colloquium PaperNonlinear partial differential equations and applications: Some nonlinear elliptic equations from geometry [O] . YanYan Li 2007

机译：非线性偏微分方程及其应用：几何学中的一些非线性椭圆方程
7. The Dirichlet problem for fully nonlinear elliptic equations non-degenerate in a fixed direction [O] . Paola Mannucci 2014

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8. On the Existence of Infinitely Many Solutions of the Dirichlet Problem for Some Nonlinear Elliptic Equations [R] . Dong, G. C., Li, S. 1980

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THE DIRICHLET PROBLEM FOR FULLY NONLINEAR ELLIPTIC EQUATIONS NON-DEGENERATE IN A FIXED DIRECTION

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