Let QT be a cylinder in ℝn+1 and x = (x′, t) ∈ ℝn×ℝ. It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator {ut - Σni, j = 1 aij (x) a.e. in Qr, u(x) = 0 on ∂Q, in the Morrey spaces Wp, λ2, 1(Q T), p ?∈ (1, ∞), λ ∈ (0, n + 2), supposing the coefficients to belong to the class of functions with vanishing mean oscillation. There are obtained a priori estimates in Morrey spaces and Hölder regularity for the solution and its spatial derivatives.

Cauchy-Dirichlet problem in Morrey spaces for parabolic equations with discontinuous coefficients

Palagachev, D. K.;
2003-01-01

Abstract

Let QT be a cylinder in ℝn+1 and x = (x′, t) ∈ ℝn×ℝ. It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator {ut - Σni, j = 1 aij (x) a.e. in Qr, u(x) = 0 on ∂Q, in the Morrey spaces Wp, λ2, 1(Q T), p ?∈ (1, ∞), λ ∈ (0, n + 2), supposing the coefficients to belong to the class of functions with vanishing mean oscillation. There are obtained a priori estimates in Morrey spaces and Hölder regularity for the solution and its spatial derivatives.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/6157
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