Solvability of boundary-value problems for quasilinear elliptic and parabolic equations in unbounded domains in classes of functions growing at infinity
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!+- u0(x)∈L2.loc(Rn):∫|x|<τu20dx⩽cτn+2mp/(p−2)∀τ<∞
Published
25.02.1995
How to Cite
Shishkov, A. E. “Solvability of Boundary-Value Problems for Quasilinear Elliptic and Parabolic Equations in Unbounded Domains in Classes of Functions Growing at Infinity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 47, no. 2, Feb. 1995, pp. 277–289, https://umj.imath.kiev.ua/index.php/umj/article/view/5413.
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Section
Research articles