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This article is cited in 1 scientific paper (total in 1 paper)
Short Notes
Anisotropic diffusion in anisotropic Stepanov spaces
V. A. Gorlov N.E. Zhukovsky and Y.A. Gagarin Air Force Academy, Voronezh, Russian Federation
Abstract:
We consider a problem on the image processing and computer vision. A wide range of methods allows to solve problems of this type. The methods of partial differential equations are the most useful and interesting ones. A non-linear diffusion takes special place in these studies. In this context, fundamental theoretical foundation is a central part of this approach. Therefore, we introduce a new functional class of spaces, formulate and prove the lemma on the equivalent norms in anisotropic Stepanov spaces. Another important result of this study is the lemma that the anisotropic Stepanov spaces are Banach. In addition, we obtain the theorem on the solvability of the equation of anisotropic diffusion in anisotropic Stepanov spaces. The results can be applied to the image processing and computer vision. Also, the obtained results open the new view to this problem.
Keywords:
diffusion, Nikol'skii spaces, anisotropic Stepanov spaces, anisotropic diffusion, differential equations.
Received: 26.02.2019
Citation:
V. A. Gorlov, “Anisotropic diffusion in anisotropic Stepanov spaces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:3 (2019), 153–160
Linking options:
https://www.mathnet.ru/eng/vyuru512 https://www.mathnet.ru/eng/vyuru/v12/i3/p153
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