User:JohnWYu

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I'm attending the course intensive course on Science, technology, society and Wikipedia for PhD students

About Me
I am a researcher with a strong focus on the field of nonlinear analysis, particularly in the realm of partial differential equations. My academic journey and professional interests revolve around several key areas in mathematics, each contributing to my overarching goal of advancing our understanding of complex mathematical phenomena.

Research Interests
1. **Normalized Solutions for Semilinear Elliptic Equations** - My research extensively explores normalized solutions to semilinear elliptic equations. These equations arise in various physical and geometric contexts, and understanding their normalized solutions helps in interpreting their physical relevance and ensuring mathematical consistency.

2. **Trudinger-Moser Inequality** - I have a keen interest in the Trudinger-Moser inequality, a critical tool in the analysis of function spaces. This inequality plays a significant role in the study of elliptic partial differential equations, particularly in cases involving critical growth conditions.

3. **Nonlinear Elliptic PDEs** - Nonlinear elliptic partial differential equations (PDEs) form the core of my research. I delve into their properties, solutions, and applications, aiming to uncover new insights and contribute to the development of robust analytical methods.

4. **Variational Methods** - Variational methods are a cornerstone of my work, providing powerful techniques to tackle complex nonlinear problems. Through these methods, I seek to establish existence, uniqueness, and multiplicity results for solutions to various classes of PDEs.

5. **Nonlinear Analysis on Manifolds** - My research also extends to nonlinear analysis on manifolds, where I investigate how geometric and topological properties of manifolds influence the behavior of nonlinear PDEs. This intersection of geometry and analysis offers rich and intriguing problems to solve.

Hobbies and Interests
Outside of my academic pursuits, I am passionate about running. I believe that physical activity not only promotes health and well-being but also fosters mental clarity and creativity. Running allows me to clear my mind, reflect on research problems, and often, some of my best ideas come to me during a long run.

Thank you for visiting my user page. I look forward to meaningful interactions and collaborations!