共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
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.
The existence of positive radial solutions of the equation -din( |Du|p-2Du)=f(u) is studied in annular domains in Rn,n≥2. It is proved that if f(0)≥0, f is somewherenegative in (0,∞), limu→0^ f‘ (u)=0 and limu→∞ (f(u)/u^p-1)=∞, then there is alarge positive radial solution on all annuli. If f(0)≤0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide. 相似文献
4.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2020,37(5):1109-1141
We study radial sign-changing solutions of a class of fully nonlinear elliptic Dirichlet problems in a ball, driven by the extremal Pucci's operators and with a power nonlinear term. We first determine a new critical exponent related to the existence or nonexistence of such solutions. Then we analyze the asymptotic behavior of the radial nodal solutions as the exponents approach the critical values, showing that new concentration phenomena occur. Finally we define a suitable weighted energy for these solutions and compute its limit value. 相似文献
5.
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
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7.
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
8.
Gleydson C. Ricarte 《Journal of Functional Analysis》2011,261(6):1624-1673
In this paper we study one-phase fully nonlinear singularly perturbed elliptic problems with high energy activation potentials, ζε(u) with ζε→δ0⋅∫ζ. We establish uniform and optimal gradient estimates of solutions and prove that minimal solutions are non-degenerated. For problems governed by concave equations, we establish uniform weak geometric properties of approximating level surfaces. We also provide a thorough analysis of the free boundary problem obtained as a limit as the ε-parameter term goes to zero. We find the precise jumping condition of limiting solutions through the phase transition, which involves a subtle homogenization process of the governing fully nonlinear operator. In particular, for rotational invariant operators, F(D2u), we show the normal derivative of limiting function is constant along the interface. Smoothness properties of the free boundary are also addressed. 相似文献
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10.
Jian Deng 《Mathematical Methods in the Applied Sciences》2012,35(13):1594-1600
In this paper, we study a nonlinear elliptic problem in an annulus domain. For which, the nonexistence of nontrivial solutions has been obtained by some authors in star‐shaped domain. Although we note that it may admit non‐trivial solutions if the domain is non‐star shaped. With the use of a variational method, we establish the existence of positive radial solutions in an annulus domain. On the basis of this, we also extend this result to the periodic problem of the corresponding degenerate parabolic problem. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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12.
Zongming Guo 《Applicable analysis》2013,92(1-4):173-189
The existence and uniqueness of positive radial solutions of the equations of the type [IML0001] in BR, p>1 with Dirichlet condition are proved for λ large enough and f satisfying a condition[IML0002] is non-decreasing on [IML0003] It is also proved that all the positive solutions in C1 0(BR) of the above equations are radially symmetric solutions for f satisfying [IML0004] and λ large enough. 相似文献
13.
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
14.
Eduardo V. Teixeira 《Journal of Differential Equations》2007,238(1):43-63
In this paper we study the existence, uniqueness and propagation of regularity to infinite order partial differential evolution equations. Our approach is essentially functional and brings interesting results even when we restrict ourselves to finite order equations. 相似文献
15.
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
16.
Rodrigo Meneses 《Journal of Mathematical Analysis and Applications》2011,376(2):514-527
In this paper, we prove that a class of parabolic equations involving a second order fully nonlinear uniformly elliptic operator has a Fujita type exponent. These exponents are related with an eigenvalue problem in all RN and play the same role in blow-up theorems as the classical p?=1+2/N introduced by Fujita for the Laplacian. We also obtain some associated existence results. 相似文献
17.
Olivier Guibé Anna Mercaldo 《Transactions of the American Mathematical Society》2008,360(2):643-669
In this paper we prove the existence of a renormalized solution to a class of nonlinear elliptic problems whose prototype is
where is a bounded open subset of , , is the so-called Laplace operator, , is a Radon measure with bounded variation on , , , and and belong to the Lorentz spaces , , and , respectively. In particular we prove the existence under the assumptions that , belongs to the Lorentz space , , and is small enough.
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19.
Qingbo Huang 《Proceedings of the American Mathematical Society》2002,130(7):1955-1959
We show that any solution to the uniformly elliptic equation must belong to , if the equation has the Liouville property.
20.
Emmanouil Milakis 《Advances in Mathematics》2008,217(3):1301-1312
We study the regularity of the solution to a fully nonlinear version of the thin obstacle problem. In particular we prove that the solution is C1,α for some small α>0. This extends a result of Luis Caffarelli of 1979. Our proof relies on new estimates up to the boundary for fully nonlinear equations with Neumann boundary data, developed recently by the authors. 相似文献