The Dirichlet Problem for Degenerate Hessian Equations

By N. Ivochkina, Neil S. Trudinger, Xu-jia Wang. 2005

93 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/93b7636d16669dbd1b7fe35ab10ea2664c75b79a

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In Applied Mathematics

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Citations in the corpus

A class of curvature type equations. (2019, background): “ Guan-Trudinger-Wang [26] and the power n−1 was also shown to be sharp by an example in [47]. For the Hessian equation, that is αℓ = 0 for 1 ≤ ℓ ≤ k−1 with k < n, estimate as (1.6) was obtained in [30] with power k − 1 and a modiﬁed example shows 4 that k − 1 is the lowest possible power in [12].”
SECOND-ORDER ESTIMATES AND REGULARITY FOR FULLY NONLINEAR ELLIPTIC EQUATIONS ON RIEMANNIAN MANIFOLDS (2012, methodology): “1) in R was treated by Caffarelli-NirenbergSpruck [5], followed by [28], [10], [33], [25] among others.”
Concavity of the Lagrangian phase operator and applications (2016, background): “Since then, the Dirichlet problem for elliptic operators with various structural constraints has been studied by many authors, including generalizations to a larger class of equations and domains [5, 11, 13, 21, 32].”
Oblique boundary value problems for augmented Hessian equations I (2015, methodology): “r from our proofs that the condition F(Γ) = (a0,∞) in F3 can be replaced by F(Γ) ⊃ (a0,∞), (assuming also F4 for (iii) and (iv)). Moreover, we can alternatively replace in Theorem 1.1, in accord with [11], the cone Γ by any convex open set D⊂ Sn, 6= Sn, with 0 ∈ ∂D, which is closed under addition of”
Convex solutions to the mean curvature flow (2004, background): “ion covers equation (5.3) as it is equivalent to a concave equation (5.4) below and so can be expressed as a Bellman equation. For Hessian equations (such as (5.4)) the proof in [20] was simpliﬁed in [16]. To apply the a priori estimates in [25] we need to write equation (5.3) as a Hessian quotient ”
The k-Hessian Equation (2009, methodology): “For the k-Hessian equation, Krylov’s proof was simplifled in [ ITW ].”