A $W^n_2$-Theory of Elliptic and Parabolic Partial Differential Systems in $C^1$ domains

Details A $W^n_2$-Theory of Elliptic and Parabolic Partial Differential Systems in $C^1$ domains A $W^n_2$-Theory of Elliptic and Parabolic Partial Differential Systems in $C^1$ domains

2010-07-22

arxiv.org/abs/1007.3826v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper second-order elliptic and parabolic partial differential systems are considered on $C^1$ 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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