Boundary value problems and duality between Lp Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains.

Título inglés Boundary value problems and duality between Lp Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains.
Título español Problemas de valor de frontera y dualidad entre problemas de Dirichlet y problemas de regularidad en Lp para sistemas parabólicos de segundo orden en dominios no cilíndricos.
Autor/es Nyström, Kaj
Organización Dep. Mat. Umea Univ., Umea, Suecia
Revista 0010-0757
Publicación 2006, 57 (1): 93-119, 15 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In this paper we consider general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylinders
Ω = {(x0,x,t) Î R x Rn-1 x R: x0 > A(x,t)}.
We prove solvability of Dirichlet, Neumann as well as regularity type problems with data in Lp and Lp1,1/2 (the parabolic Sobolev space having tangential (spatial) gradients and half a time derivative in Lp) for p Î (2 − ε, 2 + ε) assuming that A(x,·) is uniformly Lipschitz with respect to the time variable and that ||Dt1/2A||* ≤ ε0 < ∞ for ε0 small enough (||Dt1/2A||* is the parabolic BMO-norm of a half-derivative in time). We also prove a general structural theorem (duality theorem between Dirichlet and regularity problems) stating that if the Dirichlet problem is solvable in Lp with the relevant bound on the parabolic non-tangential maximal function then the regularity problem can be solved with data in Lq1,1/2(∂Ω) with q−1 + p−1 = 1. As a technical tool, which also is of independent interest, we prove certain square function estimates for solutions to the system.
Clasificación UNESCO 120220
Palabras clave español Ecuaciones parabólicas ; Problemas de valor de frontera ; Problema de Dirichlet ; Espacios LP ; Regularidad ; Medidas de Carleson ; Integrales singulares
Código MathReviews MR2206182
Código Z-Math Zbl 1092.35019
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