Geodesic
On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 437-460 
V. Yu. Shelepov. On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 437-460. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a10/
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     author = {V. Yu. Shelepov},
     title = {On boundary properties of solutions of elliptic equations in multidimensional domains representable by means of the difference of convex functions},
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     volume = {61},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The author examines the solution of a linear second order uniformly elliptic equation with variable coefficients defined inside a domain whose boundary is locally representable with the aid of the difference of convex functions (the spatial analog of Radon domain without cusps in the plane). We introduce the concept of "$p$-area integral", generalizing the known Luzin area integral. Local and integral theorems are obtained on the connection between this integral and the nontangential maximal function of the solution, and also the conditions for existence of nontangential boundary values almost everywhere and in the $L_2$-metric. Bibliography: 17 titles.

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