Necessary and sufficient conditions on solvability for Hessian inequalities
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Publication:3402170
DOI10.1090/S0002-9939-09-10032-1zbMath1180.35234OpenAlexW2022701047MaRDI QIDQ3402170
Publication date: 2 February 2010
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0002-9939-09-10032-1
Nonlinear elliptic equations (35J60) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87)
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Cites Work
- On the inequality \(\Delta u \geqq f (u)\)
- Nonexistence of positive solutions for some fully nonlinear elliptic equations
- Semilinear equations in \({\mathbb{R}}^ N\) without condition at infinity
- The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
- Hessian measures. I
- Scalar curvature and conformal deformation of Riemannian structure
- The Dirichlet problem for Hessian equations on Riemannian manifolds
- Quasiconvex functions and Hessian equations
- Existence and nonexistence of entire solutions to the logistic differential equation
- Hessian measures. III
- Classifications of nonnegative solutions to some elliptic problems.
- Boundary blow-up for differential equations with indefinite weight
- Hessian measures. II
- Optimal uniqueness theorems and exact blow-up rates of large solutions
- Existence of explosive positive solutions of quasilinear elliptic equations
- Symmetry of large solutions of nonlinear elliptic equations in a ball
- On solutions of δu=f(u)
- On the Elliptic Equations Δu = K(x)u σ and Δu = K(x)e 2u
- Classical solutions of fully nonlinear, convex, second-order elliptic equations
- Conformal invariants and partial differential equations
- Unnamed Item
- Unnamed Item
- Unnamed Item