Geodesic
A priori estimates of strong solutions of semilinear parabolic equations
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 564-572 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study an initial boundary value problem for the semilinear parabolic equation $$ \frac{\partial u}{\partial t} +\sum_{|\alpha|\le2b}a_\alpha(x,t)D^\alpha u =f(x,t,u,Du,\dots,D^{2b-1}u), $$ where the left-hand side is a linear uniformly parabolic operator of order $2b$. We prove sufficient growth conditions on the function $f$ with respect to the variables $u,Du,\dots,D^{2b-1}u$, such that the apriori estimate of the norm of the solution in the Sobolev space $W_p^{2b,1}$ is expressible in terms of the low-order norm in the Lebesgue space of integrable functions $L_{l,m}$. 
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     author = {G. G. Laptev},
     title = {A priori estimates of strong solutions of semilinear parabolic equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {564--572},
     year = {1998},
     volume = {64},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a8/}
}
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G. G. Laptev. A priori estimates of strong solutions of semilinear parabolic equations. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 564-572. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a8/

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