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math.AP2026
Sobolev--Morrey Spaces and Divergence-Form Degenerate Second-Order Elliptic Equations on Domains with Higher Co-Dimensional Boundaries
Weiyi Kong, Yoshihiro Sawano, Dachun Yang +2
In this article, we study the weighted homogeneous Sobolev--Morrey spaces on domains in with higher co-dimensional boundaries. Precisely, we systematically establish…
math.AP2026
A Counterexample to the Necessity of the Vanishing Carleson Condition for VMO Poisson Kernels
Xiaosheng Lin, Dachun Yang, Sibei Yang +2
In [Problem 3.2.23, CBMS Regional Conference Series in Mathematics 83, 1994], Kenig asked whether the vanishing Carleson condition is the necessary and sufficient for the logarithm…
math.AP2026
A Counterexample to Kenig's Interpolation Problem for Sobolev Spaces with Zero Boundary Conditions
Xiaosheng Lin, Dachun Yang, Sibei Yang +2
Let . In this article, we show that there exists a bounded domain such that, for any given $s\in(1,2)\setminus\{\frac32\}…