Renormalized and entropy solutions for the fractional p-Laplacian evolution equations

  • Kaimin Teng
  • Chao ZhangEmail author
  • Shulin Zhou


In this paper, we prove the existence and uniqueness of both nonnegative renormalized and entropy solutions for the fractional p-Laplacian evolution problems with nonnegative \(L^1\) data. In addition, we obtain the equivalence of renormalized and entropy solutions and establish a comparison result.


Fractional p-Laplacian Renormalized solutions Entropy solutions Existence Uniqueness 

Mathematics Subject Classification

Primary 35D05 Secondary 35D10 46E35 


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The authors wish to thank the anonymous reviewer for valuable comments and suggestions to improve the expressions. K. Teng was supported by the NSFC (No. 11501403) and the Shanxi Province Science Foundation for Youths (No. 2013021001-3). C. Zhang was supported by the NSFC (No. 11671111) and Heilongjiang Province Postdoctoral Startup Foundation (LBH-Q16082). S. Zhou was supported by the NSFC (Nos. 11571020, 11671021).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsTaiyuan University of TechnologyTaiyuanPeople’s Republic of China
  2. 2.Department of Mathematics, Institute for Advanced Study in MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China
  3. 3.LMAM, School of Mathematical SciencesPeking UniversityBeijingPeople’s Republic of China

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