Regularity and Capacity for the Fractional Dissipative Operator

Renjin Jiang; Jie Xiao; Dachun Yang; Zhichun Zhai

Regularity and Capacity for the Fractional Dissipative Operator

Analysis of PDEs 2013-01-03 v2 Functional Analysis

Authors: Renjin Jiang , Jie Xiao , Dachun Yang , Zhichun Zhai

Abstract

This note is devoted to exploring some analytic-geometric properties of the regularity and capacity associated to the so-called fractional dissipative operator $\partial_t+(-\Delta)^\alpha$ , naturally establishing a diagonally sharp Hausdorff dimension estimate for the blow-up set of a weak solution to the fractional dissipative equation $(\partial_t+(-\Delta)^\alpha)u(t,x)=F(t,x)$ subject to $u(0,x)=0$ .

Keywords

fractional differential equations fractional laplacian fractional calculus

Cite

@article{arxiv.1212.0744,
  title  = {Regularity and Capacity for the Fractional Dissipative Operator},
  author = {Renjin Jiang and Jie Xiao and Dachun Yang and Zhichun Zhai},
  journal= {arXiv preprint arXiv:1212.0744},
  year   = {2013}
}

Comments

22 pages, submitted

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