Results 81 to 90 of about 361,418 (224)
First‐order Sobolev spaces, self‐similar energies and energy measures on the Sierpiński carpet
Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1523-1608, September 2025.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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Communications on Pure and Applied Mathematics, Volume 78, Issue 9, Page 1783-1842, September 2025.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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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 11592-11619, August 2025.ABSTRACT We consider evolution (nonstationary) space‐periodic solutions to the n$$ n $$‐dimensional nonlinear Navier–Stokes equations of anisotropic fluids with the viscosity coefficient tensor variable in space and time and satisfying the relaxed ellipticity condition.
Sergey E. Mikhailov
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Geometric Structures in Tensor Representations (Final Release) [PDF]
, 2015 The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor ...
Falco, Antonio +2 more
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Numerical Linear Algebra with Applications, Volume 32, Issue 4, August 2025.ABSTRACT We propose an algorithm to solve optimization problems constrained by ordinary or partial differential equations under uncertainty, with additional almost sure inequality constraints on the state variable. To alleviate the computational burden of high‐dimensional random variables, we approximate all random fields by the tensor‐train (TT ...
Harbir Antil +2 more
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Dimensionality Reduction in Full‐Waveform Inversion Uncertainty Analysis
Geophysical Prospecting, Volume 73, Issue 6, July 2025.ABSTRACT The uncertainty of model parameters obtained by full‐waveform inversion can be determined from the Hessian of the least‐squares error functional. A description of uncertainty characterisation is presented that takes the null space of the Hessian into account and does not rely on the Bayesian formulation.
W. A. Mulder, B. N. Kuvshinov
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An Axiomatic Approach to Mild Distributions
AxiomsThe Banach Gelfand Triple (S0,L2,S0′) consists of the Feichtinger algebra S0(Rd) as a space of test functions, the dual space S0′(Rd), known as the space of mild distributions, and the intermediate Hilbert space L2(Rd). This Gelfand Triple is very useful
Hans G. Feichtinger
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Rough PDEs for Local Stochastic Volatility Models
Mathematical Finance, Volume 35, Issue 3, Page 661-681, July 2025.ABSTRACT In this work, we introduce a novel pricing methodology in general, possibly non‐Markovian local stochastic volatility (LSV) models. We observe that by conditioning the LSV dynamics on the Brownian motion that drives the volatility, one obtains a time‐inhomogeneous Markov process. Using tools from rough path theory, we describe how to precisely
Peter Bank +3 more
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Sub-Riemannian Geometry and Geodesics in Banach Manifolds [PDF]
The Journal of Geometric Analysis, 2019 In this paper, we define and study sub-Riemannian structures on Banach manifolds. We obtain extensions of the Chow-Rashevski theorem for exact controllability, and give conditions for the existence of a Hamiltonian geodesic flow despite the lack of a Pontryagin Maximum Principle in the infinite dimensional setting.
openaire +4 more sources
Analysis of a Radiotherapy Model for Brain Tumors
Studies in Applied Mathematics, Volume 155, Issue 1, July 2025.ABSTRACT In this work, we focus on the analytical and numerical study of a mathematical model for brain tumors undergoing radiotherapy treatment. Under certain assumptions regarding the given data in the model, we prove the existence and uniqueness of a weak nonnegative (biologically relevant) solution.
Marina Chugunova +3 more
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