Modulus of continuity of solutions to complex Hessian equations

2014/01/31 by Charabati, Mohamad · 1 citation
#32U05 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.8254

Abstract

We give a sharp estimate of the modulus of continuity of the solution to the Dirichlet problem for the complex Hessian equation of order m (1 ≤ m ≤ n) with a continuous right hand side and a continuous boundary data in a bounded strongly m-pseudoconvex domain \Om \Subset \Cⁿ. Moreover when the right hand side is in L^p(\Om) , for some p > n/m and the boundary value function is C^1,1 we prove that the solution is Hölder continuous.

Cited by

• Continuity of solutions to complex Hessian equations on compact Hermitian manifolds

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