Nonlinear potential theory on metric spaces

• Project/Area Number: 25K00211
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Okinawa Institute of Science and Technology Graduate University
• Principal Investigator: ZHOU Xiaodan 沖縄科学技術大学院大学, 距離空間上の解析ユニット, 准教授 (10871494)
• Project Period (FY): 2025-04-01 – 2028-03-31
• Project Status: Granted (Fiscal Year 2025)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2027: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2026: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000); Fiscal Year 2025: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: p-harmonic / potential theory

Outline of Research at the Start

This project is devoted to studying various properties of the solutions to p-Laplace equations on metric spaces, including a new approach to obtain the existence of solution to Dirichlet problems. The key question we want to address is reducing the Poincare inequality assumption of the space.