Mikyoung Lee, Jihoon Ok
Abstract:
We derive interior and boundary \(L^q\)-regularity estimates for double obstacle
problems involving quasilinear operators of \(p\)-Laplacian type and lower-order terms
with nonnegative potential functions satisfying a reverse Holder type condition.
We prove that the \(L^q\) norms of the gradient of a solution to the obstacle problem,
as well as the lower-order term, can be estimated by the \(L^q\) norms
of the data and the gradients of the obstacles.
Moreover, the relevant constants in the \(L^q\) estimates depend only on the constant
in the reverse Holder type condition for the potential and are independent of the
potential.
Submitted July 2, 2025. Published October 30, 2025.
Math Subject Classifications: 35J87, 35J92, 35J10, 35B65.
Key Words: Obstacle problem; Schrodinger operator; \(L^q\)-estimates; nonnegative potential; p-Laplacian.
DOI: 10.58997/ejde.2025.102
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| Mikyoung Lee Department of Mathematics and Institute of Mathematical Science Pusan National University, Busan 46241, Korea email: mikyounglee@pusan.ac.kr |
| Jihoon Ok Department of Mathematics Institute for Mathematical and Data Science Sogang University, Seoul 04107, Korea email: jihoonok@sogang.ac.kr |
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