Precise blowup rate near the boundary of boundary blowup solutions to \(k\)-Hessian equation

DOI10.1007/s42985-021-00071-1zbMath1465.35265OpenAlexW3125252666WikidataQ114216509 ScholiaQ114216509MaRDI QIDQ2022965

Kazuhiro Takimoto

Publication date: 3 May 2021

Published in: SN Partial Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42985-021-00071-1

zbMATH Keywords

blow-up\(k\)-Hessian equationuniformly \((k-1)\)-convex domain

Mathematics Subject Classification ID

Blow-up in context of PDEs (35B44) Monge-Ampère equations (35J96)

Related Items

Exact principal blowup rate near the boundary of boundary blowup solutions to \(k\)-curvature equation, Higher order estimate near the boundary of a large solution to semilinear Poisson equation with double-power like nonlinearity, Second order boundary estimate of boundary blowup solutions to \(k\)-Hessian equation

Cites Work

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• Higher order boundary estimates for blow-up solutions of elliptic equations.
• On the inequality \(\Delta u \geqq f (u)\)
• Blow-up rates of radially symmetric large solutions
• Second order estimates for boundary blow-up solutions of elliptic equations
• Boundary asymptotical behavior of large solutions to Hessian equations
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• Hessian measures. I
• Nonlinear elliptic equations with singular boundary conditions and stochastic control with state constraints. I: The model problem
• Boundary blow-up problems for Hessian equations
• Asymptotic behavior of solutions of boundary blow-up problems
• `Large' solutions of semilinear elliptic equations: Existence, uniqueness and asymptotic behaviour
• On the Dirichlet problem for Hessian equations
• The boundary blow-up rate of large solutions.
• Asymptotic behaviour of large solutions of quasilinear elliptic problems
• Boundary blow-up solutions to the \(k\)-Hessian equation with a weakly superlinear nonlinearity
• The Monge-Ampère equation with infinite boundary value
• Hessian measures. III
• On singular boundary value problems for the Monge-Ampère operator
• Uniqueness of boundary blowup solutions to \(k\)-curvature equation
• On the blow-up boundary solutions of the Monge-Ampére equation with singular weights
• Hessian measures. II
• On second-order effects in the boundary behaviour of large solutions of semilinear elliptic problems.
• Asymptotic behaviour of Hessian equation with boundary blow up
• On the Monge-Ampère equation with boundary blow-up: existence, uniqueness and asymptotics
• Optimal uniqueness theorems and exact blow-up rates of large solutions
• Solution to the boundary blowup problem for \(k\)-curvature equation
• On solutions of δu=f(u)
• SOLUTION OF THE DIRICHLET PROBLEM FOR SOME EQUATIONS OF MONGE-AMPÈRE TYPE
• On a problem of Bieberbach and Rademacher
• Weak solutions of hessian equations
• Generalised solutions of Hessian equations
• On the existence of a complete Kähler metric on non-compact complex manifolds and the regularity of fefferman's equation
• Boundary blow-up solutions to the \(k\)-Hessian equation with singular weights
• Convexity and asymptotic estimates for large solutions of Hessian equations