Existence and uniqueness of smooth solutions are proved for the capillary Christoffel-Minkowski problem, equivalent to a Hessian equation with Robin boundary condition, under a natural sufficient condition.
Geometric aspects of the theory of fully nonlinear elliptic equations
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Interior C^{2} estimates hold for semi-convex solutions of σ_{3}(D^{2}u)/σₗ(D^{2}u)=1 (l=1,2) and related sum equations in arbitrary dimensions, together with rigidity results.
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The capillary Christoffel-Minkowski problem
Existence and uniqueness of smooth solutions are proved for the capillary Christoffel-Minkowski problem, equivalent to a Hessian equation with Robin boundary condition, under a natural sufficient condition.
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Interior $C^{2}$ estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions
Interior C^{2} estimates hold for semi-convex solutions of σ_{3}(D^{2}u)/σₗ(D^{2}u)=1 (l=1,2) and related sum equations in arbitrary dimensions, together with rigidity results.