Access the full text.
Sign up today, get DeepDyve free for 14 days.
We consider a generalization of the Cheeger problem in a bounded, open set $$\Omega $$ Ω by replacing the perimeter functional with a Finsler-type surface energy and the volume with suitable powers of a weighted volume. We show that any connected minimizer A of this weighted Cheeger problem such that $$\mathcal {H}^{n-1}(A^{(1)} \cap \partial A)=0$$ H n - 1 ( A ( 1 ) ∩ ∂ A ) = 0 satisfies a relative isoperimetric inequality. If $$\Omega $$ Ω itself is a connected minimizer such that $$\mathcal {H}^{n-1}(\Omega ^{(1)} \cap \partial \Omega )=0$$ H n - 1 ( Ω ( 1 ) ∩ ∂ Ω ) = 0 , then it allows the classical Sobolev and BV embeddings and the classical BV trace theorem. The same result holds for any connected minimizer whenever the weights grant the regularity of perimeter-minimizer sets and $$\Omega $$ Ω is such that $$|\partial \Omega |=0$$ | ∂ Ω | = 0 and $$\mathcal {H}^{n-1}(\Omega ^{(1)} \cap \partial \Omega )=0$$ H n - 1 ( Ω ( 1 ) ∩ ∂ Ω ) = 0 .
Manuscripta Mathematica – Springer Journals
Published: Sep 11, 2017
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.