Displaying similar documents to “The parabolic mixed Cauchy-Dirichlet problem in spaces of functions which are hölder continuous with respect to space variables”

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

Dian K. Palagachev, Maria A. Ragusa, Lubomira G. Softova (2003)

Bollettino dell'Unione Matematica Italiana

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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.

Solvability problem for strong-nonlinear nondiagonal parabolic system

Arina A. Arkhipova (2002)

Mathematica Bohemica

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A class of q -nonlinear parabolic systems with a nondiagonal principal matrix and strong nonlinearities in the gradient is considered.We discuss the global in time solvability results of the classical initial boundary value problems in the case of two spatial variables. The systems with nonlinearities q ∈ ( 1 , 2 ) , q = 2 , q > 2 , are analyzed.