Kristály, A., Mester, Á. & Mezei, I.I. (2023) Communications in Contemporary Mathematics [Matematică, Q1]

Publicat: 19 Octombrie 2022

Kristály, A., Mester, Á. & Mezei, I.I. (2023) Sharp Morrey–Sobolev inequalities and eigenvalue problems on Riemannian–Finsler manifolds with nonnegative Ricci curvature. Communications in Contemporary Mathematics, 25(10), 2250063.

DOI: https://doi.org/10.1142/S0219199722500638

✓ Publisher: World Scientific Publications
✓ Categories: Mathematics; Mathematics, Applied
✓ Article Influence Score (AIS): 1.092 (2023) / Q1 in all categories

Abstract: Combining the sharp isoperimetric inequality established by Z. Balogh and A. Kristály [Math. Ann., in press, doi:10.1007/s00208-022-02380-1] with an anisotropic symmetrization argument, we establish sharp Morrey–Sobolev inequalities on n-dimensional Finsler manifolds having nonnegative n-Ricci curvature. A byproduct of this method is a Hardy–Sobolev-type inequality in the same geometric setting. As applications, by using variational arguments, we guarantee the existence/multiplicity of solutions for certain eigenvalue problems and elliptic PDEs involving the Finsler–Laplace operator. Our results are also new in the Riemannian setting.

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