Results 111 to 120 of about 3,258,064 (367)
First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
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
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The Cauchy problem for singularly perturbed higher-order integro-differential equations
The article is devoted to research the Cauchy problem for singularly perturbed higher-order linear integro-differential equation with a small parameter at the highest derivatives, provided that the roots of additional characteristic equation have ...
A. E. Mirzakulova+3 more
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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+2 more
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From generalized Cauchy-Riemann equations to linear algebras [PDF]
James A. Ward
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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
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The Cauchy Problem for a Hyperbolic Second Order Equation with Data on the Parabolic Line [PDF]
Murray H. Protter
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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+2 more
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In this paper, the uncertain characteristic Cauchy reaction-diffusion equation is solved by the variational iteration method. The uncertain characteristic Cauchy problem is converted to a system of characteristic Cauchy problems by parametric ...
Hamid ROUHPARVAR, Saeid ABBASBANDY
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On the uniqueness of the non-negative solution of the homogeneous Cauchy problem for a system of partial differential equations [PDF]
A. Pliś
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Quasi‐invariance of Gaussian measures for the 3d$3d$ energy critical nonlinear Schrödinger equation
Abstract We consider the 3d$3d$ energy critical nonlinear Schrödinger equation with data distributed according to the Gaussian measure with covariance operator (1−Δ)−s$(1-\Delta)^{-s}$, where Δ$\Delta$ is the Laplace operator and s$s$ is sufficiently large. We prove that the flow sends full measure sets to full measure sets. We also discuss some simple
Chenmin Sun, Nikolay Tzvetkov
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