Geodesic
On coercive solvability of parabolic equations
Matematičeskie zametki, Tome 11 (1972) no. 4, pp. 409-419 
V. P. Anosov; P. E. Sobolevskii. On coercive solvability of parabolic equations. Matematičeskie zametki, Tome 11 (1972) no. 4, pp. 409-419. http://geodesic.mathdoc.fr/item/MZM_1972_11_4_a7/
@article{MZM_1972_11_4_a7,
     author = {V. P. Anosov and P. E. Sobolevskii},
     title = {On coercive solvability of parabolic equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {409--419},
     year = {1972},
     volume = {11},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_4_a7/}
}
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%J Matematičeskie zametki
%D 1972
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study the coercive solvability of abstract differential equations of parabolic type in the spaces of L. N. Slobodetskii $W_p^\alpha$. It is established that the solution of equations with a constant operator $A$ which generates an analytic semigroup belongs to the trace space $E(\alpha,p,A)$. The results obtained are applied to the study of equations with a variable operator.