A Wⁿ₂-Theory of Elliptic and Parabolic Partial Differential Systems in C¹ domains

2010/07/22 by Kyeong-Hun Kim, Kim, Kyeong-Hun, Kijung Lee +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1007.3826

openalex publication_date 2010/07/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper second-order elliptic and parabolic partial differential systems are considered on C¹ domains. Existence and uniqueness results are obtained in terms of Sobolev spaces with weights so that we allow the derivatives of the solutions to blow up near the boundary. The coefficients of the systems are allowed to substantially oscillate or blow up near the boundary.

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