Solutions to the supercritical Lagrangian mean curvature equation in 2D exterior domains exhibit optimal asymptotic behavior at infinity under Lipschitz perturbations decaying at any positive rate.
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2026 2verdicts
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Existence and uniqueness of viscosity solutions are established for the supercritical phase Lagrangian mean curvature equation on exterior domains with perturbation decay faster than |x|^{-2}, plus the subcritical case without perturbation, for n at least 3.
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Optimal Asymptotic Behavior at Infinity of Solutions to the Lagrangian Mean Curvature Equation with Supercritical Phase in Dimension Two
Solutions to the supercritical Lagrangian mean curvature equation in 2D exterior domains exhibit optimal asymptotic behavior at infinity under Lipschitz perturbations decaying at any positive rate.
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Lagrangian Mean Curvature Equations on exterior domains
Existence and uniqueness of viscosity solutions are established for the supercritical phase Lagrangian mean curvature equation on exterior domains with perturbation decay faster than |x|^{-2}, plus the subcritical case without perturbation, for n at least 3.