| Abstract: |
| We present sharp Morrey-Sobolev inequalities (i.e., in the case $p>n$) on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature. For this purpose, we elaborate suitable anisotropic symmetrization arguments by applying the sharp isoperimetric inequality available on these spaces. We also provide a Hardy-type inequality within the same geometric setting. As application, by using variational arguments, we guarantee the existence & multiplicity of solutions for certain elliptic PDEs involving the Finsler-Laplace operator. Our results are also new in the Riemannian setting. Talk based on Kristaly A, Mester A, Mezei I. I, Sharp Morrey-Sobolev inequalities and eigenvalue problems on Riemannian- Finsler manifolds with nonnegative Ricci curvature, Commun. Contemp. Math, 25 (2023), no. 10, Paper No. 2250063. |
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