We consider regular oblique derivative problem in cylinder Q(T) = Omega x (0, T), Omega subset of R(n) for uniformly parabolic operator B = D(t)- Sigma(n)(i, j=1) a(ij) (x)D(ij) with VMO principal coefficients. Its unique strong solvability is proved inManuscr. Math. 203-220 (2000), when Bu is an element of L(p)(Q(T)), p is an element of (1, infinity). Our aim is to show that the solution belongs to the generalized Sobolev- Morrey space W(p,omega)(2,1)(Q(T)), when B(u) is an element of L(p,omega)(Q(T)), p is an element of (1, infinity), omega(x, r) : R(+)(n+1) -> R(+). For this goal an a priori estimate is obtained relying on explicit representation formula for the solution. Analogous result holds also for the Cauchy-Dirichlet problem.
Morrey-type regularity of the solutions to parabolic problems with discontinuous data
SOFTOVA Lyoubomira
2011
Abstract
We consider regular oblique derivative problem in cylinder Q(T) = Omega x (0, T), Omega subset of R(n) for uniformly parabolic operator B = D(t)- Sigma(n)(i, j=1) a(ij) (x)D(ij) with VMO principal coefficients. Its unique strong solvability is proved inManuscr. Math. 203-220 (2000), when Bu is an element of L(p)(Q(T)), p is an element of (1, infinity). Our aim is to show that the solution belongs to the generalized Sobolev- Morrey space W(p,omega)(2,1)(Q(T)), when B(u) is an element of L(p,omega)(Q(T)), p is an element of (1, infinity), omega(x, r) : R(+)(n+1) -> R(+). For this goal an a priori estimate is obtained relying on explicit representation formula for the solution. Analogous result holds also for the Cauchy-Dirichlet problem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
