Continuity of weak solutions to an elliptic problem on p$$ p $$‐fractional Laplacian

In this paper, we study an elliptic variational problem regarding the p$$ p $$‐fractional Laplacian in ℝN$$ {\mathrm{\mathbb{R}}}^N $$ on the basis of recent result which generalizes some nice published work, and then give some sufficient conditions under which some weak solutions to our...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2023-08, Vol.46 (12), p.12660-12674
Main Authors: Chen, Wei, Han, Qi, Zhan, Guoping
Format: Article
Language:English
Subjects:
elliptic partial differential equation
p$$ p $$‐fractional Laplacian
variational method
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Summary:In this paper, we study an elliptic variational problem regarding the p$$ p $$‐fractional Laplacian in ℝN$$ {\mathrm{\mathbb{R}}}^N $$ on the basis of recent result which generalizes some nice published work, and then give some sufficient conditions under which some weak solutions to our studied elliptic variational problem are continuous in ℝN$$ {\mathrm{\mathbb{R}}}^N $$. In the final appendix, we correct the proofs of two published lemmas for 1
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9203