Concavity of the Lagrangian phase operator and applications

Concavity of the Lagrangian phase operator and applications 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 $${\mathbb {R}}^{n}$$ R n or $${\mathbb {C}}^n$$ C n , 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 ) π 2 and boundary data $$\varphi $$ φ if and only if there exists a subsolution. Calculus of Variations and Partial Differential Equations Springer Journals

Concavity of the Lagrangian phase operator and applications

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Springer Berlin Heidelberg
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Mathematics; Analysis; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Theoretical, Mathematical and Computational Physics
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