If the smooth vector fields X1,…,Xm and their commutators span the tangent space at every point in Ω⊆RN for any fixed m≤N, then we establish the full interior regularity theory of quasi-linear equations ∑i=1mXi⁎Ai(X1u,…,Xmu)=0 with p-Laplacian type growth condition. In other words, we show that a weak solution of the equation is locally C1,α.
Giovanna Citti, Shirsho Mukherjee (2022). Regularity of quasi-linear equations with H??rmander vector fields of step two. ADVANCES IN MATHEMATICS, 408, 1-66 [10.1016/j.aim.2022.108593].
Regularity of quasi-linear equations with H??rmander vector fields of step two
Giovanna Citti;Shirsho Mukherjee
2022
Abstract
If the smooth vector fields X1,…,Xm and their commutators span the tangent space at every point in Ω⊆RN for any fixed m≤N, then we establish the full interior regularity theory of quasi-linear equations ∑i=1mXi⁎Ai(X1u,…,Xmu)=0 with p-Laplacian type growth condition. In other words, we show that a weak solution of the equation is locally C1,α.File in questo prodotto:
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