Geodesic
Boundary Properties of Solutions to Second-Order Parabolic Equations in Domains with Special Symmetry
Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 386-402

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We consider the first boundary-value problem for second-order nondivergent parabolic equations with, in general, discontinuous coefficients. We study the regularity of a boundary point assuming that in a neighborhood of this point the boundary of the domain is a surface of revolution. We prove a necessary and sufficient regularity condition in terms of parabolic capacities; for the heat equation this condition coincides with Wiener"s criterion. 
@article{MZM_2001_70_3_a6,
     author = {I. T. Mamedov},
     title = {Boundary {Properties} of {Solutions} to {Second-Order} {Parabolic} {Equations} in {Domains} with {Special} {Symmetry}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {386--402},
     publisher = {mathdoc},
     volume = {70},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a6/}
}
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I. T. Mamedov. Boundary Properties of Solutions to Second-Order Parabolic Equations in Domains with Special Symmetry. Matematičeskie zametki, Tome 70 (2001) no. 3, pp. 386-402. http://geodesic.mathdoc.fr/item/MZM_2001_70_3_a6/