Isolated singularities of solutions of linear and semilinear elliptic equations with singular drifts

초록

We study isolated singularities of solutions of linear and semilinear elliptic equations in divergence form with singular drifts. First, extending a classical result for isolated singularities of harmonic functions, we establish a removable isolated singularity theorem for linear equations with drifts bin Lq0 (BR; Rn) for some q0 >= n, where n >= 2 is the dimension. Then this theorem is applied to prove removability theorems for isolated singularities of solutions of some semilinear equations with drifts in Lq0 (BR; Rn). One novelty of our results is that the critical case q0 = n is allowed for removable singularity theorems for both linear and semilinear equations. Moreover, our methods of proofs rely only on interior W1,q-estimates for solutions on annuli and Lq-estimates for their traces on spheres but not pointwise estimates like the maximum principle, which can be thus applied to linear and nonlinear systems. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

키워드