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My research interests lie in analysis and partial differential equations:
Regularity theory of degenerate elliptic and parabolic equations;
Calculus of variations and minimax theory.
Publications:
Publications:
Harnack inequality for singular or degenerate parabolic equations in non-divergence form (with S. Cho and T. Phan), J. Differential Equations 457 (2026), 113997. [arXiv: 2409.09437], [Journal].
Well-posedness for a class of parabolic equations with singular-degenerate coefficients (with T. Phan) [arXiv:2510.20051], submitted.
On $W^{2, \varepsilon}$ estimates for a class of singular-degenerate parabolic equations (with T. Phan) [arXiv:2601.04324], submitted.
Projects in Preparation:
Projects in Preparation:
Well-posedness for a class of parabolic equations with singular-degenerate coefficients: the conormal problem.
Research Statement:
Research Statement:
Research statement_(Junyuan Fang).pdfPage updated
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