Corrigendum

This article refers to:

Boundedness of Solutions to Anisotropic Variational Problems

Article title: “Boundedness of solutions to anisotropic variational problems”

Author: Angela Alberico

Journal: Communications in Partial Differential Equations

Bibliometrics: Volume 36, pages 470–486

DOI: 10.1080/03605302.2010.509768

We correct a flaw in inequality (2.14) and an error in the proof of Theorem 4.1 of our paper. Inequality (2.14) should be replaced by

for some constant σ > 0. After this change the proof of Theorem 3.1 is completely analogous.

The text from Eq. (4.8) to the end of the proof of Theorem 4.1 should be replaced by the following one.

(4.8)

Ineqality 4.7 yields

(4.9)

From (4.9), through (4.8), we obtain that

(4.10)

Let S(t) be defined as in (3.17). Since S is an increasing function and lim _t→+∞S(t) = + ∞, for any fixed c > 0 and k > 1, there exists a positive number t₁ such that

An analogous argument as in the proof of (3.19) yields that

(4.11)

for t > max {t₀, s₀, t₁}. Inequalities (4.10) and (4.11) imply that

(4.12)

whence

(4.13)

By Jensen's inequality and (2.12) with g = u, we deduce that

(4.14)

From (4.13) and (4.14), through the anisotropic Pólya-Szegö principle (2.14), one infers that

(4.15)

namely, inequality (3.11) of the proof of Theorem 3.1, with c = S(t₁). The conclusion hence follows through the same arguments as in the proof of Theorem 3.1.