Correction to: Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains (Numerische Mathematik, (2022), 150, 2, (299-371), 10.1007/s00211-021-01256-x)

We are grateful to Andreas Rathsfeld (WIAS, Berlin) for drawing our attention to an error in the statement of one of the results of this paper. The error is in the statement of part (b) of Theorem 3.2, which claims more than is true. This has minor implications for where this result is used later in the paper, including in the statement of Theorem 3.17. We provide, for the convenience of the reader, corrected statements of Theorems 3.2 and 3.17 at the end of this erratum. First, we provide a list of the six corrections as follows: 1. The statement of part (b) of Theorem 3.2 should read (with no initial “For some (Formula presented.) ”): (b) (Formula presented.) 2. In the proof of part (b) of Theorem 3.2, equation (3.17) on Page 330 should be replaced by (Formula presented.) the “Since (Formula presented.) is convex” on the line above (3.17) should be replaced by “Since (Formula presented.) is convex”, and the “for some (Formula presented.) ” on the line below (3.17) should be deleted. 3. In the statement of Theorem 3.17, in the line before equation (3.34) on page 337, the “for some (Formula presented.) ” should be deleted, and (3.34) should read: (Formula presented.) 4. In the proof of Theorem 3.17, starting in the last paragraph on Page 337, the “for some (Formula presented.) ” should be deleted, the penultimate displayed equation on Page 337 should read (Formula presented.) the last displayed equation on Page 337 should read (Formula presented.) and the last sentence of the proof, on Page 338, should read as follows: For every (Formula presented.) , (Formula presented.) , for some (Formula presented.) and (Formula presented.) , so that, by (2.5), (Formula presented.) 5. The final sentence of Section 3 on page 338 no longer makes sense and should be deleted. 6. The first displayed equation of the proof of Theorem 1.3 on page 360 should read (Formula presented.) Here are the new versions of Theorems 3.2 and 3.17, incorporating the above corrections: [Localisation result for general Lipschitz case] Suppose that (Formula presented.) is a bounded Lipschitz domain and let (Formula presented.) (a) For some (Formula presented.) , (Formula presented.) (b) (Formula presented.) [Localisation for locally-dilation-invariant surfaces and polyhedra] Suppose that (Formula presented.) , the boundary of the bounded Lipschitz domain (Formula presented.) , is locally dilation invariant and (Formula presented.) is a set of generalised vertices of (Formula presented.). (This is the case, in particular, if (Formula presented.) is a polygon or a polyhedron and (Formula presented.) is the set of vertices in the normal sense.) Then (Formula presented.) and (Formula presented.).