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

Dian K. PalagachevMaria A. RagusaLubomira G. Softova — 2003

Bollettino dell'Unione Matematica Italiana

Let Q T be a cylinder in R n + 1 and x = x , t R n × R . It is studied the Cauchy-Dirichlet problem for the uniformly parabolic operator u t - i , j = 1 n a i j x D i j u = f x q.o. in  Q T , u x = 0 su  Q T , in the Morrey spaces W p , λ 2 , 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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