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).

Appendix A contains many misprints. However it is ineffective in our paper,  as one can directly utilize Proposition 1.5.1 from the monograph "Stable solutions of elliptic partial differential equations" by L. Dupaigne, in conjunction with Theorem 1.2 in the paper "Stable solutions to semilinear elliptic equations are smooth up to dimension 9" (Acta Math. 224 (2020), no. 2, 187-252), to directly deduce the C^2 estimate stated at the end in the proof of Proposition 2.3. Note that since we have proven f'(u_\infty) is in L^1 locally, then the cuf-off functions in the book of  Dupaigne are allowed  to pass to the limit via Lebesgue's dominated convergence theorem, which tells that u is stable.