Results 31 to 40 of about 13,144,199 (261)
The regularity for the Monge-Ampere equation and the k-Hessian equation
, 2022 In this thesis, we study some important nonlinear partial differential equations, including the Monge-Ampere equation, the k-Hessian equation and the k-curvature equation. There are four problems studied in this thesis.
Yating Wu (1853134)
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Singular solutions to k-Hessian equations with fast-growing nonlinearities
Nonlinear Analysis, 2022 Version accepted in ...
João Marcos do Ó +2 more
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A short note on Harnack inequality for k-Hessian equations with nonlinear gradient terms [PDF]
Opuscula MathematicaIn this short note we study a Harnack inequality for \(k\)-Hessian equations that involve nonlinear lower-order terms which depend on the solution and its gradient.
Ahmed Mohammed, Giovanni Porru
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Nonlinear Analysis, 2018 In this paper, we establish the existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations in a ball.
Jianxin He +3 more
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Journal of Mathematical Analysis and Applications, 2021 We establish for $2 \le k \le n-1$ the strict concavity of the function $f_k(λ)=\log(σ_k(λ))$ on a subset of the positive cone $Γ_n=\{λ=(λ_{1}, λ_{2}, \cdots,λ_{n})\in \mathbb{R}^n; λ_j>0,j=1,\cdots, n\}$ where $σ_{k}(λ)$ is the basic symmetric polynomial of degree $k,$ $2 \leq k \leq n.$ Then we apply the result to study the so-called $d-$concavity
Bang Tran Van +3 more
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Existence of radial solutions to biharmonic k-Hessian equations
Journal of Differential Equations, 2015 This work presents the construction of the existence theory of radial solutions to the elliptic equation \begin{equation}\nonumber Δ^2 u = (-1)^k S_k[u] + λf(x), \qquad x \in B_1(0) \subset \mathbb{R}^N, \end{equation} provided either with Dirichlet boundary conditions \begin{eqnarray}\nonumber u = \partial_n u = 0, \qquad x \in \partial B_1(0), \end ...
Carlos Escudero, Pedro J. Torres
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ある種の放物型 k-Hessian 方程式に対する Bernstein 型定理 [PDF]
, 2015 We are concerned with the characterization of entire solutions to the parabolic k-Hessian equation of the form −utFk(D2u) = 1 in Rn ×(−∞, 0]. We prove that for 1 ≤ k ≤ n, any strictly convex-monotone solution u = u(x, t) ∈ C4,2(Rn × (−∞, 0]) to −utFk(D2u)
Nakamori, Saori
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k-Hessian curvature type equations in space forms
Electronic Journal of Differential Equations, 2022 In this article, we study closed star-shaped (eta, k)-convex hypersurfaces in space forms satisfying a class of k-Hessian curvature type equations. Firstly, using the maximum principle, we obtain a priori estimates for the class of Hessian curvature type equations.
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Angewandte Chemie, EarlyView.A photoswitchable ligand was used to trigger conformational changes within the thrombin binding aptamer DNA G‐Quadruplex. These reversible ligand driven rearrangements were examined by time‐resolved NMR experiments to gain insight of the dynamic folding landscape of the G‐quadruplex.
Jason Martins +2 more
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Extremal functions for a supercritical k-Hessian inequality of Sobolev-type [PDF]
, 2020 Our main purpose in this paper is to investigate a supercritical Sobolev-type inequality for the $k$-Hessian operator acting on $\Phi^{k}_{0,\mathrm{rad}}(B)$, the space of radially symmetric $k$-admissible functions on the unit ball $B\subset\mathbb{R}^{
Ubilla, Pedro +3 more
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