Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian

In this paper we prove the Hölder regularity of bounded, uniformly continuous, viscosity solutions of some degenerate fully nonlinear equations in the Heisenberg group.1991 Mathematics Subject Classification. 35D40, 35B65, 35H20. Key words and phrases. Heisenberg group, viscosity solutions, Theorem of the sums. The author is supported by MURST, Italy, and GNAMPA project 2017: Regolarità delle soluzioni viscose per equazioni a derivate parziali non lineari degeneri.

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Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian

Abstract: Abstract. In this paper we prove the existence of nonsmooth viscosity solutions for Dirichlet problems involving elementary symmetric functions of the eigenvalues of the complex Hessian.2010 MSC: 32U05, 35D40, 35J70.

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References 17 publications

Solvability of the Neumann problem for complex hessian equations in balls

Solvability of the Neumann problem for complex hessian equations in balls

Hölder behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group

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