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Title: On nondivergence form linear parabolic and elliptic equations with degenerate coefficients

Abstract: We establish the unique solvability in weighted mixed-norm Sobolev spaces for a class of degenerate parabolic and elliptic equations in the upper half space. The operators are in nondivergence form, with the leading coefficients given by x2daij, where aijis bounded, uniformly nondegenerate, and measurable in (t, xd) except add, which is measurable in tor xd. In the remaining spatial variables, they have weighted small mean oscillations. In addition, we investigate the optimality of the function spaces associated with our results. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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