Erratum

Some typos in the published papers are listed here:

1. Paper "Some sharp Sobolev regularity for inhomogeneous infinity Laplace equation in plane" (J. Math. Pures Appl. 132(2019) 483–521). 

On line -4 of Page 493, we applied Holder inequality to the power 2p and 2p/(2p-1) there. The power of the integrand in the second bracket should be 2p/(2p-1). 

2. Paper "Strong stability for the Wulff inequality with a crystalline norm" (Comm. Pure Appl. Math. 75 (2022), no. 2, 422–446).

       On line 4 of Page 431, it should be "\partial H_{ij}^a \subset \partial V_i^a \cap \partial V_j^a \cap \partial K^a" in the first term. Namely "\cap \partial K^a" is missing there. 

3. Paper "Optimal regularity & Liouville property for stable solutions to semilinear elliptic equations in R^n with n\ge 10" (Anal. PDE 17 (2024), no. 9, 3335–3353). 

On line -2 of Page 3344, the left-hand side should be \|u-u_{B_{1/2}}\|_{M^{p_n, \beta}(B_{1/2})}. Namely one should minus a constant to apply the Poincare-type inequality. 

4. Paper "Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations. "(Comm. Pure Appl. Math. 77 (2024), no. 1, 3–36).

    In the previous version, the proof of Proposition A.1 was not complete. Indeed, Lemma A.2 was proved only for estimates centered at the origin, and Footnote 9 claimed that the same estimates hold at every point; however, no complete proof was provided for this extension. Indeed, Lemma A.2 can be restricted to estimates at the origin, and H\"older regularity at arbitrary points is obtained by combining the results in [7,10] with the new version of Lemma A.2. This avoids the need to extend Lemma A.2 to arbitrary centers and yields a complete proof of Proposition A.1.