Some Issues on the p-Laplace Equation in Cylindrical Domains

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. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

Intermediate Address Space: virtual memory optimization of heterogeneous architectures for cache-resident workloads

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The increasing demand for computing power and the emergence of heterogeneous computing architectures have driven the exploration of innovative techniques to address current limitations in both the compute and memory subsystems. One such solution is the use ...

2024

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

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We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

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Anomalous dissipation and other non-smooth phenomena in fluids

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The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

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Touch and Closeness in Naturally Organized Activities

Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...

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Entrepreneurial Opportunities and Threats in the Era of Grand Societal Challenges

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We live in an era defined by attempts to grapple with an ever-expanding array of grand societal challenges (GCs). These challenges comprise transformational social and environmental issues, such as environmental degradation and global pandemics, and the cr ...

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Virtual Memory (VM) is a critical programming abstraction that is widely used in various modern computing platforms. With the rise of datacenter computing and birth of planet-scale online services, the semantic and capacity requirements from memory have ev ...

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Dynamical Low-Rank Approximation for Stochastic Differential Equations

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American Mathematical Society (AMS)2024

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

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The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

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Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

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We present outlier-free isogeometric Galerkin discretizations of eigenvalue problems related to the biharmonic and the polyharmonic operator in the univariate setting. These are Galerkin discretizations in certain spline subspaces that provide accurate app ...

Elsevier Science Sa2023

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