On the Dirichlet problem for a class of fully nonlinear elliptic equations
Based on the asymptotic property of the level hypersurfaces of f , we show that the solvability of Dirichlet problem for the fully nonlinear elliptic equation with Γ = Γ n is closely related to the existence of a C -subsolution introduced by Székelyhidi (J Differ Geom 109: 337–378, 2018) of a rescal...
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Veröffentlicht in: | Calculus of variations and partial differential equations 2021-10, Vol.60 (5), Article 162 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | Based on the asymptotic property of the level hypersurfaces of
f
, we show that the solvability of Dirichlet problem for the fully nonlinear elliptic equation with
Γ
=
Γ
n
is closely related to the existence of a
C
-subsolution introduced by Székelyhidi (J Differ Geom 109: 337–378, 2018) of a rescaled equation. For the complex Monge–Ampère equation and complex Hessian equations the gradient estimate established in previous works (Błocki, Math Ann 344: 317–327, 2009; Hanani, J Funct Anal 137: 49–75, 1996; Guan and Li, Adv Math 225: 1185–1223, 2010; Zhang, Int Math Res Not 2010: 3814–3836, 2010) also follows as a consequence of our argument. Also, the existence and regularity of
admissible
solutions to Dirichlet problem for fully nonlinear elliptic equations on compact Kähler manifolds of nonnegative orthogonal bisectional curvature are obtained. |
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ISSN: | 0944-2669 1432-0835 |
DOI: | 10.1007/s00526-021-02012-7 |