Abstract Let X1,X2,…,Xq be a system of real smooth vector fields satisfying Hörmander's rank condition in a bounded domain Ω of . Let be a symmetric, uniformly positive definite matrix of real functions defined in a domain . For operators of kind we prove local a-priori estimates of Schauder-type, in the natural (parabolic) Ck,α(U) spaces defined by the vector fields Xi and the distance induced by them. Namely, for aij, bi, cCk,α(U) and U′U, we prove uCk+2,α(U′)c{HuCk,α(U)+uL∞(U)}.
Schauder estimates for parabolic nondivergence operators of Hörmander type
BRANDOLINI, Luca;
2007-01-01
Abstract
Abstract Let X1,X2,…,Xq be a system of real smooth vector fields satisfying Hörmander's rank condition in a bounded domain Ω of . Let be a symmetric, uniformly positive definite matrix of real functions defined in a domain . For operators of kind we prove local a-priori estimates of Schauder-type, in the natural (parabolic) Ck,α(U) spaces defined by the vector fields Xi and the distance induced by them. Namely, for aij, bi, cCk,α(U) and U′U, we prove uCk+2,α(U′)c{HuCk,α(U)+uL∞(U)}.File allegato/i alla scheda:
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