A Note on Very Weak Solutions for a Class of Nonlinear Elliptic Equations

Authors

  • Li Juling Department of Applied Mathematics, North China Electric Power University, Baoding, P.R.China
  • Gao Hongya Department of Mathematics, Hebei University, Baoding, P. R.China

DOI:

https://doi.org/10.5644/SJM.03.1.05

Keywords:

Very weak solution, Hodge decomposition, regular domain

Abstract

We prove a new a priori estimate for very weak solutions of a class of nonlinear elliptic equations.

 

2000 Mathematics Subject Classification. 30C62, 35J60

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References

T. Iwaniec, p–harmonic tensors and quasiregular mapping, Anal. Math., 136 (1992), 589–624.

T. Iwaniec and C. Sbordone, Weak minima of variational integrals, J. Reine Angew. Math., 454 (1994), 143–161.

Juha Kinnunen and Shulin Zhou, A note on very weak p-harmonic mapping, Electron. J. Differ. Equ., No. 25 (1997), 1–4.

Yu. G. Reshetnyak, Space Mapping with Bounded Distortion, Translation of Mathematical Monographs, 73, American Mathematical Society, Providence, Rhode Island, 1989.

D. Giachetti, F. Leonetti and R. Schianchi, On the regularity of very weak minima, Proc. R. Soc. Edinb., Sect. A, 126 (1996), 287–296.

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Published

12.06.2024

How to Cite

Juling, L., & Hongya, G. (2024). A Note on Very Weak Solutions for a Class of Nonlinear Elliptic Equations. Sarajevo Journal of Mathematics, 3(1), 41–45. https://doi.org/10.5644/SJM.03.1.05

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