Concavity of the Lagrangian phase operator and applications

By Tristan C. Collins, Sebastien Picard, Xuan Wu. 2016

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We study the Dirichlet problem for the Lagrangian phase operator, in both the real and complex setting. Our main result states that if $$\Omega $$Ω is a compact domain in $${\mathbb {R}}^{n}$$Rn or $${\mathbb {C}}^n$$Cn, then there exists a solution to the Dirichlet problem with right-hand side h(x) satisfying $$|h(x)| > (n-2)\frac{\pi }{2}$$|h(x)|>(n-2)π2 and boundary data $$\varphi $$φ if and only if there exists a subsolution.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/224f528360c27d4ab9a853cd16f333d2d7615851