Conformally invariant fully nonlinear elliptic equations and isolated singularities

By Yanyan Li. 2005

70 citations recorded by the source corpus.

Abstract We study properties of solutions with isolated singularities to general conformally invariant fully nonlinear elliptic equations of second order. The properties being studied include radial symmetry and monotonicity of solutions in the punctured Euclidean space and the asymptotic behavior of solutions in a punctured ball. Some results apply to more general situations including more general fully nonlinear elliptic equations of second order, and some have been used in a companion paper to establish comparison principles and Liouville type theorems for degenerate elliptic equations.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/130b8cbb6cc6d53bab5c2eec0f1f275d80ff5272

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities (2019, background): “2) and provides an expansion of uafter the order of u∗. The main theorems of [5] and [28] were completely extended to solutions of second order fully nonlinear Yamabe equations by Li-Li [30], Y.Y. Li [31], Chang-Han-Yang [10] and Han-Li-Teixeira [23]. There are also works on studying similar problem”
Local gradient estimates of solutions to some conformally invariant fully nonlinear equations (2006, background): “1 is along the line of [24], which makes use of ideas developed in [20] and [23] in treating the isolated singularity of u at ∞.”
Some remarks on singular solutions of nonlinear elliptic equations. I (2009, methodology): “In [14], (4) was also established for some special classes of F (x, u,∇u,∇2u) which include F (∇u,∇2u), again for superharmonic u; see Theorem 1.”
Fundamental solutions of homogeneous fully nonlinear elliptic equations (2009, background): “We also note that in the last several years there has been a great amount of interest of singular solutions of conformally invariant fully nonlinear equations (we refer to [19, 18, 5] and the references in these works).”
Asymptotic behavior of solutions to the σk-Yamabe equation near isolated singularities (2009, methodology): “3 of [49]: Theorem E ([49]) Suppose that u ∈ C(2)(B2 \{0}) is a positive solution to (8′).”
Asymptotic Expansions of Solutions of the Yamabe Equation and the σk‐Yamabe Equation near Isolated Singular Points (2019, methodology): “For n=2 < k < n, according to an estimate proved by Gursky and Viacolvsky [8] and Li [11], ' D w decays as e 0t , as t ! 1.”