Fractional Sobolev norms and structure of Carnot-Carathéodory balls for Hörmander vector fields

• Autorzy: Daniele Morbidelli
• Języki publikacji: EN

Abstrakty

EN

We study the notion of fractional $L^p$-differentiability of order $s∈(0,1)$ along vector fields satisfying the Hörmander condition on $ℝ^n$. We prove a modified version of the celebrated structure theorem for the Carnot-Carathéodory balls originally due to Nagel, Stein and Wainger. This result enables us to demonstrate that different $W^{s,p}$-norms are equivalent. We also prove a local embedding $W^{1,p} ⊂ W^{s,q}$, where q is a suitable exponent greater than p.

Kategorie tematyczne

• 35J70: Degenerate elliptic equations
• 46E35: Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 139
• Numer: 3
• Strony: 213-244

Daty

wydano

2000

otrzymano

1998-11-23

poprawiono

2000-01-05

Twórcy

autor

Daniele Morbidelli

• Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40127 Bologna, Italy

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