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A concept of weak Riesz energy with application to condensers with touching plates
Analysis and Mathematical Physics ( IF 1.7 ) Pub Date : 2020-09-08 , DOI: 10.1007/s13324-020-00384-1
Natalia Zorii

We proceed further with the study of minimum weak Riesz energy problems for condensers with touching plates, initiated jointly with Fuglede (Potential Anal 51:197–217, 2019). Having now added to the analysis constraint and external source of energy, we obtain a Gauss type problem, but with weak energy involved. We establish sufficient and/or necessary conditions for the existence of solutions to the problem and describe their potentials. Treating the solution as a function of the condenser and the constraint, we prove its continuity relative to the vague topology and the topologies determined by the weak and standard energy norms. We show that the criteria for the solvability thus obtained fail in general once the problem is reformulated in the setting of standard energy, thereby justifying an advantage of weak energy when dealing with condensers with touching plates.

中文翻译:

Riesz能量弱的概念及其在带有接触板的冷凝器中的应用

我们将与Fuglede共同启动关于接触板式冷凝器的最小弱Riesz能量问题的研究(Potential Anal 51:197-217,2019)。现在增加了分析约束和外部能源,我们得到了一个高斯型问题,但是涉及的能量很弱。我们为存在问题的解决方案建立了充分和/或必要的条件,并描述了其潜力。将解决方案视为电容器和约束的函数,我们证明了其相对于由弱能级和标准能级确定的模糊拓扑和拓扑的连续性。我们表明,一旦在标准能量的设置中重新提出了问题,由此获得的可溶性标准通常就会失败,
更新日期:2020-09-08
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