共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we prove a Hadamard property and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with a gradient term, both in the whole space and in an exterior domain. 相似文献
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We study Hessian fully nonlinear uniformly elliptic equations and show that the second derivatives of viscosity solutions of those equations (in 12 or more dimensions) can blow up in an interior point of the domain. We prove that the optimal interior regularity of such solutions is no more than C1+?, showing the optimality of the known interior regularity result. The same is proven for Isaacs equations. We prove the existence of non-smooth solutions to fully nonlinear Hessian uniformly elliptic equations in 11 dimensions. We study also the possible singularity of solutions of Hessian equations defined in a neighborhood of a point and prove that a homogeneous order 0<α<1 solution of a Hessian uniformly elliptic equation in a punctured ball should be radial. 相似文献
3.
Marcelo Montenegro 《Journal of Functional Analysis》2010,259(2):428-452
We establish Lipschitz regularity for solutions to a family of non-isotropic fully nonlinear partial differential equations of elliptic type. In general such a regularity is optimal. No sign constraint is imposed on the solution, thus limiting free boundaries may have two-phases. Our estimates are then employed in combination with fine regularizing techniques to prove existence of viscosity solutions to singular nonlinear PDEs. 相似文献
4.
Antonio Tarsia 《Journal of Global Optimization》2008,40(1-3):443-453
We give a short survey of the Campanato near operators theory and of its applications to fully nonlinear elliptic equations. 相似文献
5.
本文证明了:若完全非线性一致抛物型方程ut-F(D2u)=0有Liouville性质,则它的任何C1 1,1 1/2(Q1)粘性解u-定属于C2 α,1 α/2(Q1/2)且ut一定属于 相似文献
6.
CHENCAISHENG WANGYUANMING 《高校应用数学学报(英文版)》1995,10(2):167-178
By the Schauder-Tychonoff fixed-point theorem, we investigate the existence and asymptotic behavior of positive radial solutions of fully nonlinear elliptic equations in R^n. We give some sufficient conditions to guarantee the existence of bounded and unbounded radial solutions and consider the nonexistence of positive solution in R^n. 相似文献
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POSITIVESOLUTIONSANDBIFURCATIONOFFULLYNONLINEARELLIPTICEQUATIONSINVOLVINGSUPER-CRITICALSOBOLEVEXPONENTS¥QUCHANGZHENG(屈长征)(Ins... 相似文献
10.
For a wide class of nonlinearities satisfying
we show that any nonnegative solution of the quasilinear equation over the entire must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.
0$\space in $(0,a)$\space and $f(u)<0$\space in $(a,\infty)$ ,}\end{displaymath}">
we show that any nonnegative solution of the quasilinear equation over the entire must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.
11.
Qingbo Huang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(7):1869-1902
We develop interior and regularity theories for -viscosity solutions to fully nonlinear elliptic equations , where T is approximately convex at infinity. Particularly, regularity theory holds if operator T is locally semiconvex near infinity and all eigenvalues of are at least as . regularity for some Isaacs equations is given. We also show that the set of fully nonlinear operators of regularity theory is dense in the space of fully nonlinear uniformly elliptic operators. 相似文献
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È. I. Semenov 《Siberian Mathematical Journal》2008,49(1):166-174
We obtain new formulas for the exact analytic solutions to the nonautonomous elliptic Liouville equation in the two-dimensional coordinate space with the free function dependent specially on an arbitrary harmonic function. We present new exact solutions to the wave Liouville equation with two arbitrary functions, providing original formulas for the general solution for the classical (autonomous) and wave Liouville equations. Some equivalence transformations are presented for the elliptic Liouville equation depending on conjugate harmonic functions. In particular, we indicate a transformation that reduces the equation under study to an autonomous form. 相似文献
14.
Smail Djebali 《Journal of Mathematical Analysis and Applications》2007,333(2):863-870
In this note we investigate the existence of positive solutions vanishing at +∞ to the elliptic equation Δu+f(x,u)+g(|x|)x⋅∇u=0, |x|>A>0, in Rn (n?3) under mild restrictions on the functions f, g. 相似文献
15.
Jingxue Yin Jing Li Chunhua Jin 《Journal of Mathematical Analysis and Applications》2009,360(1):119-129
This paper is concerned with the existence and comparison principle of classical solutions for a class of fully nonlinear degenerate parabolic equations. 相似文献
16.
Hongjie Dong Hong Zhang 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(4):971-992
We obtain Dini type estimates for a class of concave fully nonlinear nonlocal elliptic equations of order with rough and non-symmetric kernels. The proof is based on a novel application of Campanato's approach and a refined estimate in [9]. 相似文献
17.
G. Gripenberg 《Journal of Mathematical Analysis and Applications》2009,352(1):175-183
Sufficient conditions are given for the solutions to the (fully nonlinear, degenerate) elliptic equation F(x,u,Du,D2u)=0 in Ω to satisfy |u(x)−u(y)|?Cα|x−y| for some α∈(0,1) when x∈Ω and y∈∂Ω. 相似文献
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Roberto Argiolas 《Ricerche di matematica》2008,57(1):1-12
We prove regularity of Lipschitz free boundaries of one phase problems for fully nonlinear elliptic operators where the mean curvature
appears in the free boundary condition.
相似文献
20.
We prove that a viscosity solution of a uniformly elliptic, fully nonlinear equation is C2,α on the complement of a closed set of Hausdorff dimension at most ? less than the dimension. The equation is assumed to be C1, and the constant ? > 0 depends only on the dimension and the ellipticity constants. The argument combines the W2,? estimates of Lin with a result of Savin on the C2,α regularity of viscosity solutions that are close to quadratic polynomials. © 2012 Wiley Periodicals, Inc. 相似文献