Regularity of Solutions to an Integral Equation on a Half-Space R+n

DOI: 10.4236/apm.2013.31A021   PDF   HTML     5,373 Downloads   8,867 Views  

Abstract

In this paper, we discuss the integral equation on a half space R+n

where is the reflection of the point x about the . We study the regularity for the positive solutions of (0.1). A regularity lifting method by contracting operators is used in proving the boundedness of solutions, and the Lipschitz continuity is derived by combinations of contracting and shrinking operators introduced by Ma-Chen-Li ([1]).



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L. Cao and Z. Dai, "Regularity of Solutions to an Integral Equation on a Half-Space R+n," Advances in Pure Mathematics, Vol. 3 No. 1A, 2013, pp. 153-158. doi: 10.4236/apm.2013.31A021.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[6] L. Ma and D. Chen, “Radial Symmetry and Uniqueness of Non-Negative Solutions to an Integral System,” Mathematical and Computer Modelling, Vol. 49, No. 1-2, 2009, pp. 379-385. doi:10.1016/j.mcm.2008.06.010
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[8] W. Chen and C. Li, “Methods on Nonlinear Elliptic Equations. AIMS Series on Differential Equations and Dynamical Systems,” American Institute of Mathematical Science (AIMS), Springfield, 2010.

  
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