Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior
From MaRDI portal
Publication:831048
DOI10.1515/anona-2020-0139zbMath1465.35262OpenAlexW3081422257MaRDI QIDQ831048
Publication date: 10 May 2021
Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/anona-2020-0139
Boundary value problems for second-order elliptic equations (35J25) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Second-order elliptic systems (35J47) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Monge-Ampère equations (35J96)
Related Items (14)
The first initial-boundary value problem of parabolic Monge-Ampère equations outside a bowl-shaped domain ⋮ Radial solutions for fully nonlinear elliptic equations of Monge-Ampère type ⋮ New results of positive doubly periodic solutions to telegraph equations ⋮ On the solutions to weakly coupled system of \(\boldsymbol{k_i}\)-Hessian equations ⋮ Existence and nonexistence of entire \(k\)-convex radial solutions to Hessian type system ⋮ Existence and boundary asymptotic behavior of strictly convex solutions for singular Monge-Ampère problems with gradient terms ⋮ The existence and multiplicity of \(k\)-convex solutions for a coupled \(k\)-Hessian system ⋮ Existence and asymptotic behavior of strictly convex solutions for singular \(k\)-Hessian equations with nonlinear gradient terms ⋮ The existence of radial \(k\)-admissible solutions for \(n\)-dimension system of \(k\)-Hessian equations ⋮ Eigenvalue problems for singular \(p\)-Monge-Ampère equations ⋮ \(k\)-convex solutions for multiparameter Dirichlet systems with \(k\)-Hessian operator and Lane-Emden type nonlinearities ⋮ A class of singular \(k_{i}\)-Hessian systems ⋮ Positive solutions of singular multiparameter \(p\)-Laplacian elliptic systems ⋮ A class of singular coupled systems of superlinear Monge-Ampère equations
Cites Work
- Unnamed Item
- Unnamed Item
- A uniqueness result for a semipositone \(p\)-Laplacian problem on the exterior of a ball
- Uniqueness of nonnegative solutions for semipositone problems on exterior domains
- Two Whyburn type topological theorems and its applications to Monge-Ampère equations
- A priori bounds and existence of positive solutions for semilinear elliptic systems
- On a power-type coupled system of Monge-Ampère equations
- Existence and multiplicity of solutions for asymptotically linear noncooperative elliptic systems
- Triple nontrivial radial convex solutions of systems of Monge-Ampère equations
- Symmetry breaking via Morse index for equations and systems of Hénon-Schrödinger type
- Structure of positive radial solutions of semilinear elliptic equations
- \(C^{1}\) regularity of solutions of the Monge-Ampère equation for optimal transport in dimension two
- Existence and non-existence of solutions for a class of Monge-Ampère equations
- Uniqueness of the solution of a semilinear boundary value problem
- Existence of multiple solutions to the equations of Monge-Ampère type
- Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball
- Solvability for two-point boundary value problems
- Entire solutions blowing up at infinity for semilinear elliptic systems.
- On a class of semilinear elliptic systems.
- Existence and uniqueness for a class of quasilinear elliptic boundary value problems.
- Existence of entire large positive solutions of semilinear elliptic systems
- Elliptic partial differential equations of second order
- Quasilinear elliptic systems in divergence form associated to general nonlinearities
- New results of coupled system of \(k\)-Hessian equations
- Sharp conditions for the existence of boundary blow-up solutions to the Monge-Ampère equation
- The Monge-Ampère equation with infinite boundary value
- A priori estimates and existence for elliptic systems via bootstrap in weighted Lebesgue spaces
- Classical solutions of singular Monge-Ampère equations in a ball
- Existence and nonexistence to exterior Dirichlet problem for Monge-Ampère equation
- Uniqueness of positive solutions for a class of semilinear elliptic systems
- On singular boundary value problems for the Monge-Ampère operator
- On the blow-up boundary solutions of the Monge-Ampére equation with singular weights
- \(W^{2,1}\) regularity for solutions of the Monge-Ampère equation
- Existence and uniqueness of positive solutions of semilinear elliptic systems
- Analysis of positive radial solutions for singular superlinear \(p\)-Laplacian systems on the exterior of a ball
- Boundary blow-up solutions to the Monge-Ampère equation: sharp conditions and asymptotic behavior
- Hamiltonian elliptic systems: a guide to variational frameworks
- Bifurcation for strongly indefinite functional and applications to Hamiltonian system and noncooperative elliptic system
- Blow-up solutions for fully nonlinear equations: existence, asymptotic estimates and uniqueness
- Boundary regularity for the Monge-Ampère and affine maximal surface equations
- Global smoothness for a singular Monge-Ampère equation
- Uniqueness of positive radial solutions for infinite semipositone \(p\)-Laplacian problems in exterior domains
- Existence and multiplicity of positive radial solutions for singular superlinear elliptic systems in the exterior of a ball
- Entire solutions of quasilinear elliptic systems on Carnot groups
- On the Monge-Ampère equation with boundary blow-up: existence, uniqueness and asymptotics
- Boundary behavior of large solutions for semilinear elliptic equations with weights
- On the number of positive solutions for nonlinear elliptic equations when a parameter is large
- On the existence of solutions to the Monge-Ampère equation with infinite boundary values
- On boundary blow-up problems for the complex Monge-Ampère equation
- Convex Solutions of systems of Monge-Amp\`ere equations
- On the Number of Positive Solutions of Weakly Non-Linear Elliptic Equations when a Parameter is Large
- The dirichlet problem for nonlinear second-order elliptic equations I. Monge-ampégre equation
- The dirichlet problem for nonlinear second-order elliptic equations. II. Complex monge-ampère, and uniformaly elliptic, equations
- Positive splutions of semilinear elliptic systems
- On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u)
- Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large
- Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations
- Uniqueness of non-negative solutions for a semipositone problem with concave nonlinearity
- Pointwise 𝐶^{2,𝛼} estimates at the boundary for the Monge-Ampère equation
- A coupled system of k‐Hessian equations
This page was built for publication: Convex solutions of Monge-Ampère equations and systems: existence, uniqueness and asymptotic behavior
