Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity |
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Authors: | A E Shishkov |
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Institution: | 1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk
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Abstract: | For divergent elliptic equations with the natural energetic spaceW p m (Ω),m≥1,p>2, we prove that the Dirichlet problem is solvable in a broad class of domains with noncompact boundaries if the growth of the right-hand side of the equation is determined by the corresponding theorem of Phragmén-Lindelöf type. For the corresponding parabolic equation, we prove that the Cauchy problem is solvable for the limiting growth of the initial function % MathType!MTEF!2!1!+- $$u_0 (x) \in L_{2.loc} (R^n ): \int\limits_{|x|< \tau } {u_0^2 dx \leqslant c\tau ^{n + 2mp/(p - 2)} \forall \tau< \infty } $$ |
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