The Neumann Problem for Hessian Equations

By Xinan Ma, Guohuan Qiu. Communications in Mathematical Physics, 2015

50 citations recorded by the source corpus.

In this paper, we prove the existence of a classical solution to a Neumann boundary value problem for Hessian equations in uniformly convex domain. The method depends upon the establishment of a priori derivative estimates up to second order. So we give an affirmative answer to a conjecture of N. Trudinger in 1987.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/209dfb1f74e3075862e650eb418c067d9b8b7f53

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In Applied Mathematics

1. Feida Jiang
2. Neil S. Trudinger
3. Xu-jia Wang
4. Robert J. McCann
5. Alessio Figalli
6. Grégoire Loeper
7. Giuseppe Mingione
8. Young-Heon Kim

In Computational Theory and Mathematics

1. Feida Jiang
2. Neil S. Trudinger
3. Xu-jia Wang
4. Bo Guan

Citations in the corpus

• Oblique boundary value problems for augmented Hessian equations I (2015, background): “Recently the Neumann problem for the standard k-Hessian equation has been studied in uniformly convex domains in [29].”