Results 41 to 50 of about 683 (263)

On the Dirichlet Problem For Degenerate Elliptic Equations

Publications of the Research Institute for Mathematical Sciences, 1987
In this paper a class of linear and degenerate elliptic problems is considered: the operator is uniformly elliptic in a neighbourhood of a domain of \({\mathbb{R}}\) but it degenerates in a very precise form on an interior part of it. A suitable associated weighted Sobolev space is introduced; this allows to describe and solve uniquely the ...
openaire   +3 more sources

Chiral Phase Change Nanomaterials

Advanced Functional Materials, EarlyView.
This work demonstrates reversible, non‐volatile phase transitions in chiral Ge2${\rm Ge}_2$Sb2${\rm Sb}_2$Te5${\rm Te}_5$ (GST) nanohelices for high‐speed optical modulation of chirality and dynamic control of the state of polarization (SOP). The chiral nanostructures are fabricated using a highly directional, wafer‐scale physical vapor deposition ...
Joshua A. Burrow, Md Shah Alam, Riad Yahiaoui, Evan M. Smith, Ryan Laing, Jules Gardener, Thomas A. Searles, Piyush J. Shah, Shivashankar Vangala, Joshua R. Hendrickson, Andrew M. Sarangan, Imad Agha   +11 more
wiley   +1 more source

A boundary value problem for the fourth-order degenerate equation of the mixed type

Қарағанды университетінің хабаршысы. Математика сериясы
Many problems in mechanics, physics, and geophysics lead to solving partial differential equations that are not included in the known classes of elliptic, parabolic or hyperbolic equations.
J.A. Otarova
doaj   +1 more source

From Photoalignment to Structured Light: Liquid Crystal Platforms for Beam Shaping and Complex Wavefronts

Advanced Functional Materials, EarlyView.
Photoaligned and photopatterned liquid crystal platforms provide programmable control of optical phase, polarization, and spin‐orbit interactions, enabling compact generation of structured light and complex wavefronts. This review highlights how tailored molecular orientations transform simple beams into designed optical fields, opening versatile ...
Le Zhou, Tingjun Zhong, Sijie Liu, Pouya Nosratkhah, Ke Xu, Yuzhen Zhao, Kristiaan Neyts   +6 more
wiley   +1 more source

Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations

Вестник Самарского университета: Естественнонаучная серия
We consider a class of second order elliptic equations in divergence form with non-uniform exponential degeneracy. The method used is based on the fact that the degeneracy rates of the eigenvalues of the matrix ||aij(x)||(function λi(x)) are not the ...
Sarvan T. Huseynov, Mushfig J. Aliyev
doaj   +1 more source

Microfluidic Nano‐Assembly of Red‐Blood‐Cell (RBC) Lipids and Components for Engineering Extracellular Vesicles

Advanced Healthcare Materials, EarlyView.
Engineered red blood cell‐derived extracellular vesicles (eRBCEVs) are synthesized via controlled microfluidic assembly from native RBC lipids, enabling tunable encapsulation of proteins, nucleic acids, nanoparticles, and viral vectors. The platform demonstrates reproducible nanoscale architecture, preserved membrane composition, and functional cargo ...
Chiranth K. Nagaraj, Xilal Y. Rima, Kim T. Nguyen, Courtney Culkins, Nana Boateng, Jacob Doon‐Ralls, Alejandro Bresolin, Xin Huang, Hong Li, Vahedi Amid, Ajeet Pal Singh, Dharti Shantaram, Anastasiia Amari, Mangesh D. Hade, Nicholas R. Merriam, Zachary D. Schultz, Scott Q. Harper, Nizar Y. Saad, Setty M. Magaña, Willa A. Hsueh, Rachel E. Kopec, Blaise R. Kimmel, Andre F. Palmer, Eduardo Reátegui   +23 more
wiley   +1 more source

𝐿∞-Solutions for Some Nonlinear Degenerate Elliptic Equations

International Journal of Differential Equations, 2011
We are interested in the existence of solutions for Dirichlet problem associated to the degenerate quasilinear elliptic equations −∑𝑛𝑗=1𝐷𝑗[𝜔2(𝑥)𝒜𝑗(𝑥,𝑢,∇𝑢)]+𝜔1(𝑥)𝑔(𝑥,𝑢(𝑥))+𝐻(𝑥,𝑢,∇𝑢)𝜔2(𝑥)=𝑓(𝑥),onΩ in the setting of the weighted Sobolev spaces W01,𝑝(Ω,𝜔1,𝜔2)
Albo Carlos Cavalheiro
doaj   +1 more source

Sodium Alginate‐Based Submucosal Lifting Hydrogel for Endoscopic Mucosal Resection and Endoscopic Submucosal Dissection

Advanced Healthcare Materials, EarlyView.
A biocompatible sodium alginate‐based hydrogel is developed as a next‐generation submucosal lifting agent intended for EMR and ESD. The optimized formulation exhibits a composition devoid of endotoxins, high viscosity, demonstrates reliable injectability, and ensures prolonged mucosal elevation.
Iram Maqsood, Venkata S. Akshintala, Surya T. Evani, Rebecca A. Krimins, Yihan Wang, Keith Freel, Ahmed Ibrahim, Saowanee Ngamruengphong, Mouen Khashab, Stephen W. Hoag   +9 more
wiley   +1 more source

Patient‐Derived 3D Heart‐On‐a‐Chip Model of Dilated Cardiomyopathy With Embedded Bead‐Based Mapping of Tissue Contractility

Advanced Healthcare Materials, EarlyView.
A heart‐on‐a‐chip model of dilated cardiomyopathy is developed from patient‐derived induced pluripotent stem cells. The model recapitulates key disease phenotypes and enables functional assessment through integrated bead‐based tracking and pillar deflection measurements.
Ali Mousavi, Ludovic Mouttet, Shihao Cui, Yasaman Hekmatnia, Mehran Mottahedi, Ida Derish, Naimeh Rafatian, Mark Aurousseau, Gregor Andelfinger, Renzo Cecere, Houman Savoji   +10 more
wiley   +1 more source

Multiplicity of weak solutions to degenerate weighted quasilinear elliptic equations with nonlocal terms and variable exponents

Electronic Journal of Qualitative Theory of Differential Equations
This paper studies the existence and multiplicity of weak solutions to degenerate weighted quasilinear elliptic equations with nonlocal nonlinearities and variable exponents.
Khaled Kefi
doaj   +1 more source