Alexandru Kristály, Ágnes Mester, Ildikó I. Mezei
Published 2021-07-01Version 1
By using a sharp isoperimetric inequality and an anisotropic symmetrization argument, we establish Morrey-Sobolev and Hardy-Sobolev inequalities on $n$-dimensional Finsler manifolds having nonnegative $n$-Ricci curvature; in some cases we also discuss the sharpness of these functional inequalities. 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.
Semilinear elliptic equations on manifolds with nonnegative Ricci curvature
Gradient Bounds and Liouville theorems for Quasi-linear equations on compact Manifolds with nonnegative Ricci curvature
Sharp Hardy and Hardy--Sobolev inequalities with point singularities on the boundary
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