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September 22, 2025Transactions of the American Mathematical Society

Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients

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Authors

HDHongjie DongJRJunhee Ryu

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Overview

Research reveals well-posedness and regularity of solutions in mixed-norm Sobolev spaces, indicating new insights on parabolic equations.

Key Points

  • The study finds well-posedness and regularity of solutions in weighted mixed-norm Sobolev spaces.
  • Key evidence shows bounded mean oscillations for coefficients, confirming regularity under specific conditions.
  • Analysis involves adding the well-posedness of degenerate parabolic and elliptic equations in divergence form using spatial variables.
  • Results support new methods for assessing solutions with degenerate coefficients, expanding current mathematical frameworks.

Cite This Study

Dong et al. (2025) studied this question.

synapsesocial.com/papers/68d46fdc31b076d99fa6a6d3https://doi.org/10.1090/tran/9527
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