We derive weak solvability and higher integrability of the spatial gradient of solutions to Cauchy-Dirichlet problem for divergence form quasi-linear parabolic equations {u(t) - div (a(ij)(x, t, u)D(j)u + a(i)(x, t, u)) = b(x, t, u, Du) in Q, u = 0 on partial derivative(p)Q, where Q is a cylinder in R(n) x (0, T) with Reifenberg flat base Omega. The principal coefficients a(ij)(x, t, u) of the uniformly parabolic operator are supposed to have small BMO norms with respect to (x, t) while the nonlinear terms a(i)(x, t, u) and b(x, t, u, Du) support controlled growth conditions.

Quasilinear divergence form parabolic equations in Reifenberg flat domains / Palagachev, Dk; Softova, Lg. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 31:4(2011), pp. 1397-1410. [10.3934/dcds.2011.31.1397]

Quasilinear divergence form parabolic equations in Reifenberg flat domains

Palagachev, DK;
2011-01-01

Abstract

We derive weak solvability and higher integrability of the spatial gradient of solutions to Cauchy-Dirichlet problem for divergence form quasi-linear parabolic equations {u(t) - div (a(ij)(x, t, u)D(j)u + a(i)(x, t, u)) = b(x, t, u, Du) in Q, u = 0 on partial derivative(p)Q, where Q is a cylinder in R(n) x (0, T) with Reifenberg flat base Omega. The principal coefficients a(ij)(x, t, u) of the uniformly parabolic operator are supposed to have small BMO norms with respect to (x, t) while the nonlinear terms a(i)(x, t, u) and b(x, t, u, Du) support controlled growth conditions.
2011
Quasilinear divergence form parabolic equations in Reifenberg flat domains / Palagachev, Dk; Softova, Lg. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 31:4(2011), pp. 1397-1410. [10.3934/dcds.2011.31.1397]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/6326
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