Geodesic
Anisotropic diffusion in anisotropic Stepanov spaces
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 3, pp. 153-160

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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: Nikol'skii spaces, anisotropic Stepanov spaces, differential equations.
Mots-clés : diffusion, anisotropic diffusion 
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     author = {V. A. Gorlov},
     title = {Anisotropic diffusion in anisotropic {Stepanov} spaces},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {153--160},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2019_12_3_a12/}
}
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V. A. Gorlov. Anisotropic diffusion in anisotropic Stepanov spaces. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 12 (2019) no. 3, pp. 153-160. http://geodesic.mathdoc.fr/item/VYURU_2019_12_3_a12/