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ABSTRACT We consider the Dirichlet problem for the complex Hessian equation of order . First, we give a specific estimate on the modulus of continuity of the solution with a… Click to show full abstract
ABSTRACT We consider the Dirichlet problem for the complex Hessian equation of order . First, we give a specific estimate on the modulus of continuity of the solution with a continuous right-hand side and a continuous boundary data in a strongly m-hyperconvex Lipschitz domain in . Then we prove the Hölder continuity of the solution. Also, in the m-hyperconvex domain, we prove that if the boundary value function can be continuously extended to a m-subharmonic function on Ω, then the same complex equation is solvable.
Keywords:
complex hessian;
equation hyperconvex;
hessian equation;
hyperconvex domain;
regularity complex;
equation
Journal Title: Complex Variables and Elliptic Equations
Year Published: 2018
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Journal Title: Complex Variables and Elliptic Equations
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!