В. И. Богачев, Andrey Pilipenko, A. V. Shaposhnikov
Abstract
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We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.
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We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.
Key concepts: Sobolev space, Mathematics, Domain (mathematical analysis), Interpolation space, Sobolev spaces for planar domains, Regular polygon, Sobolev inequality, Pure mathematics