On the First Eigenvalue of the Degenerate pp -Laplace Operator in Non-convex Domains / V. M. Gol’dshtein, V. A. Pchelintsev, A. D. Ukhlov
Уровень набора: Integral Equations and Operator TheoryЯзык: английский.Резюме или реферат: In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate p-Laplace operator, p>2 , in a large class of non-convex domains. This study is based on applications of the geometric theory of composition operators on Sobolev spaces that permits us to estimate constants of the Poincare–Sobolev inequalities. On this base we obtain lower estimates of the first non-trivial eigenvalues for Ahlfors-type domains (i.e. quasidiscs). This class of domains includes some snowflake-type domains with fractal boundaries..Примечания о наличии в документе библиографии/указателя: [References: 45 tit.].Аудитория: .Тематика: электронный ресурс | труды учёных ТПУ | elliptic equations | Sobolev spaces | эллиптические уравнения | пространство Соболева | квазиконформные отображения | операторы | Composition operators Ресурсы он-лайн:Щелкните здесь для доступа в онлайнНет реальных экземпляров для этой записи
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[References: 45 tit.]
In this paper we obtain lower estimates of the first non-trivial eigenvalues of the degenerate p-Laplace operator, p>2 , in a large class of non-convex domains. This study is based on applications of the geometric theory of composition operators on Sobolev spaces that permits us to estimate constants of the Poincare–Sobolev inequalities. On this base we obtain lower estimates of the first non-trivial eigenvalues for Ahlfors-type domains (i.e. quasidiscs). This class of domains includes some snowflake-type domains with fractal boundaries.
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