Abstract The classical Faber–Krahn inequality asserts that balls (uniquely) minimize the first
eigenvalue of the Dirichlet Laplacian among sets with given volume. In this article we prove …

The quantitative isoperimetric inequality and related topics | Bulletin of Mathematical Sciences
Skip to main content Advertisement Springer Nature Link Account Menu Find a journal Publish …

The affine L p Pólya–Szegö principle significantly strengthens the classical Pólya–Szegö
principle. It is an open problem whether there exists an affine Orlicz Pólya–Szegö principle …

Let Ω⊂ R d be an open set, and consider the Laplacian operator−∆ on Ω under various
boundary conditions. When the relevant spectrum happens to be discrete, it is an interesting …

The aims of this paper are to develop the LYZ ellipsoid and Petty projection body for log-
concave functions, which correspond to the LYZ ellipsoid and Petty projection body for …

In this article, we present two different approaches for obtaining quantitative inequalities in
the context of parabolic optimal control problems. Our model consists of a linearly controlled …

The Petty projection inequality for sets of finite perimeter is proved. Our approach is based
on Steiner symmetrization. Neither the affine Sobolev inequality nor the functional …

These lecture notes contain the material that I presented in two summer courses in 2013,
one at the Carnegie Mellon University and the other one in a CIME school at Cetraro. The …

We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the
$ p $-Laplacian. Quantitative stability is achieved here via integral identities based on the …

In this paper, the Orlicz centroid function for log-concave functions is introduced. A
rearrangement inequality of the Orlicz centroid function for log-concave functions is …