Simulating Terahertz Plasma Oscillations in Transistors
                        
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            Abstract We extend the Calderón–Zygmund theory for nonlocal equations tostrongly coupled system of linear nonlocal equations {\mathcal{L}^{s}_{A}u=f}, where the operator {\mathcal{L}^{s}_{A}}is formally given by \mathcal{L}^{s}_{A}u=\int_{\mathbb{R}^{n}}\frac{A(x,y)}{|x-y|^{n+2s}}\frac{(x-%y)\otimes(x-y)}{|x-y|^{2}}(u(x)-u(y))\,dy. For {0more » « less<1}and {A:\mathbb{R}^{n}\times\mathbb{R}^{n}\to\mathbb{R}}taken to be symmetric and serving asa variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier–Lamé linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if {A(\,\cdot\,,y)}is uniformly Holder continuous and {\inf_{x\in\mathbb{R}^{n}}A(x,x)>0}, then for {f\in L^{p}_{\rm loc}}, for {p\geq 2}, the solution vector {u\in H^{2s-\delta,p}_{\rm loc}}for some {\delta\in(0,s)}.
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            This Editorial introduces the Virtual Issue ‘Nectar and nectaries’ that includes the following papers: Ballarinet al.(2024), Griersonet al.(2024), Grof‐Tiszaet al.(2025), Landucci & Vannette (2025), Liaoet al.(2025), MacNeillet al.(2025), Magneret al.(2023, 2024, 2025), Minet al.(2019), Mouet al.(2025), Parkinsonet al.(2025), Quevedo‐Caraballoet al.(2025), Ramoset al.(2025), Romero‐Bravo & Castellanos (2024), Soareset al.(2025), Turneret al.(2025), Zhaiet al.(2025), Zhanget al.(2020). Access the Virtual Issue atwww.newphytologist.com/virtualissues.more » « less
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