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Mixed boundary value problems for the Helmholtz equation in a model 2D angular domain
Georgian Mathematical Journal ( IF 0.8 ) Pub Date : 2020-06-01 , DOI: 10.1515/gmj-2019-2031 Roland Duduchava 1 , Medea Tsaava 2
Georgian Mathematical Journal ( IF 0.8 ) Pub Date : 2020-06-01 , DOI: 10.1515/gmj-2019-2031 Roland Duduchava 1 , Medea Tsaava 2
Affiliation
Abstract The purpose of the present research is to investigate model mixed boundary value problems (BVPs) for the Helmholtz equation in a planar angular domain Ω α ⊂ ℝ 2 {\Omega_{\alpha}\subset\mathbb{R}^{2}} of magnitude α. These problems are considered in a non-classical setting when a solution is sought in the Bessel potential spaces ℍ p s ( Ω α ) {\mathbb{H}^{s}_{p}(\Omega_{\alpha})} , s > 1 p {s>\frac{1}{p}} , 1 < p < ∞ {1
中文翻译：
模型二维角域中亥姆霍兹方程的混合边值问题
摘要 本研究的目的是研究 Helmholtz 方程在平面角域 Ω α ⊂ ℝ 2 {\Omega_{\alpha}\subset\mathbb{R}^{2} } 量级为 α。当在贝塞尔势空间 ℍ ps ( Ω α ) {\mathbb{H}^{s}_{p}(\Omega_{\alpha})} , s > 1 p {s>\frac{1}{p}} , 1 < p < ∞ {1
更新日期：2020-06-01
中文翻译：
模型二维角域中亥姆霍兹方程的混合边值问题
摘要 本研究的目的是研究 Helmholtz 方程在平面角域 Ω α ⊂ ℝ 2 {\Omega_{\alpha}\subset\mathbb{R}^{2} } 量级为 α。当在贝塞尔势空间 ℍ ps ( Ω α ) {\mathbb{H}^{s}_{p}(\Omega_{\alpha})} , s > 1 p {s>\frac{1}{p}} , 1 < p < ∞ {1
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