Potential estimates for a class of fully nonlinear elliptic equations

By D. Labutin. 2002

162 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d22ba9d0ea38fc90f5ddd0f96a859cd8489eb82e

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The k-Hessian Equation (2009, methodology): “The Wolfi potential estimate and H˜older continuity of k-admissible solutions in x9 were proved in [ Ld ].”
A priori estimates for complex Hessian equations (2011, methodology): “The real Hessian equation has been studied in many papers, for example [Caffarelli et al. 1985; Ivochkina et al. 2004; Krylov 1995; Trudinger 1995; Trudinger and Wang 1999; Labutin 2002; Chou and Wang 2001; Urbas 2001].”
Singular quasilinear and Hessian equations and inequalities (2009, methodology): “In the present paper, we use extensively dyadic models, and various global and local Wolff’s potential estimates obtained in [12], [13], [21], [22], [25], [26], along with fundamental weak continuity theorems for quasilinear and Hessian equations [32]–[34].”
Sharp criteria of Liouville type for some nonlinear systems (2013, unknown): “[23], [25], [26] and [44]).”
Gradient estimates via linear and nonlinear potentials (2010, unknown): “More precisely, in [20] – and in [35,22], where a different and interesting approach was later developed – we can find the estimate ∣∣u(x)∣∣ c( ∫–”
Wiener regularity for large solutions of nonlinear equations (2003, methodology): “In [43], the Wiener criterion was proved for Hessian equations.”
Quasilinear and Hessian equations of Lane-Emden type (2005, background): “operators. In particular, (1.13) holds if f 2 L ”
On the weak continuity of elliptic operators and applications to potential theory (2002, methodology): “The two main ingredients in our approach, which follow from our treatment of the fully nonlinear Hessian operators in [45, 46, 47], together with that of Labutin [30], are a weak convergence result and a pointwise potential estimate for subharmonic functions.”