Results 121 to 130 of about 19,135,649 (331)

Nodal properties for p-Laplacian systems

Electronic Journal of Differential Equations, 2017
We consider a system of differential equations involving the p-Laplacian. We prove the existence of oscillatory solutions with prescribed numbers of zeros, and show that the solutions satisfy the Dirichlet boundary conditions when the large parameters
Yan-Hsiou Cheng, Wei-Chuan Wang
doaj  

Efficient and model‐agnostic parameter estimation under privacy‐preserving post‐randomization data

Canadian Journal of Statistics, EarlyView.
Abstract Balancing data privacy with public access is critical for sensitive datasets. However, even after de‐identification, the data are still vulnerable to, for example, inference attacks (by matching some keywords with external datasets). Statistical disclosure control (SDC) methods offer additional protection, and the post‐randomization method ...
Qinglong Tian, Jiwei Zhao
wiley   +1 more source

First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet

Communications on Pure and Applied Mathematics, EarlyView.
Abstract For any p∈(1,∞)$p \in (1,\infty)$, we construct p$p$‐energies and the corresponding p$p$‐energy measures on the Sierpiński carpet. A salient feature of our Sobolev space is the self‐similarity of energy. An important motivation for the construction of self‐similar energy and energy measures is to determine whether or not the Ahlfors regular ...
Mathav Murugan, Ryosuke Shimizu
wiley   +1 more source

Uniqueness on average of large isoperimetric sets in noncompact manifolds with nonnegative Ricci curvature

Communications on Pure and Applied Mathematics, EarlyView.
Abstract Let (Mn,g)$(M^n,g)$ be a complete Riemannian manifold which is not isometric to Rn$\mathbb {R}^n$, has nonnegative Ricci curvature, Euclidean volume growth, and quadratic Riemann curvature decay. We prove that there exists a set G⊂(0,∞)$\mathcal {G}\subset (0,\infty)$ with density 1 at infinity such that for every V∈G$V\in \mathcal {G}$ there ...
Gioacchino Antonelli, Marco Pozzetta, Daniele Semola   +2 more
wiley   +1 more source

Maximum principles for the fractional p-Laplacian and symmetry of solutions [PDF]

arXiv, 2017
In this paper, we consider nonlinear equations involving the fractional p-Laplacian $$ (-\lap)_p^s u(x)) \equiv C_{n,s,p} PV \int_{\mathbb{R}^n} \frac{|u(x)-u(y)|^{p-2}[u(x)-u(y)]}{|x-z|^{n+ps}} dz= f(x,u).$$ We prove a {\em maximum principle for anti-symmetric functions} and obtain other key ingredients for carrying on the method of moving planes ...
arxiv  

On a problem of lower limit in the study of nonresonance

Abstract and Applied Analysis, 1997
We prove the solvability of the Dirichlet problem {−Δpu=f(u)+h   in   Ω,              u=0                     on  ∂Ω for every given h, under a condition involving only the asymptotic behaviour of the potential F of f with respect to the first ...
A. Anane, O. Chakrone
doaj   +1 more source

On classification of global dynamics for energy‐critical equivariant harmonic map heat flows and radial nonlinear heat equation

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We consider the global dynamics of finite energy solutions to energy‐critical equivariant harmonic map heat flow (HMHF) and radial nonlinear heat equation (NLH). It is known that any finite energy equivariant solutions to (HMHF) decompose into finitely many harmonic maps (bubbles) separated by scales and a body map, as approaching to the ...
Kihyun Kim, Frank Merle
wiley   +1 more source

Remarks on uniqueness results of the first eigenvalue of the p-Laplacian [PDF]

, 1988
Guy Barles
openalex   +1 more source

Boundary conditions and universal finite‐size scaling for the hierarchical |φ|4$|\varphi |^4$ model in dimensions 4 and higher

Communications on Pure and Applied Mathematics, EarlyView.
Abstract We analyse and clarify the finite‐size scaling of the weakly‐coupled hierarchical n$n$‐component |φ|4$|\varphi |^4$ model for all integers n≥1$n \ge 1$ in all dimensions d≥4$d\ge 4$, for both free and periodic boundary conditions. For d>4$d>4$, we prove that for a volume of size Rd$R^{d}$ with periodic boundary conditions the infinite‐volume ...
Emmanuel Michta, Jiwoon Park, Gordon Slade   +2 more
wiley   +1 more source