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Volume 40, Issue 2
Hölder Regularity for the Linearized Porous Medium Equation in Bounded Domains

Tianling Jin & Jingang Xiong

DOI: 10.4208/ata.OA-2023-0015

Anal. Theory Appl., 40 (2024), pp. 111-171.

Published online: 2024-07

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  • Abstract

In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the linearized fast diffusion equation and the linearized porous medium equation with the homogeneous Dirichlet boundary condition. We prove the Hölder regularity of their weak solutions.

  • Keywords

Singular parabolic equations, degenerate parabolic equations, regularity, porous medium equations.

  • AMS Subject Headings

35B65, 35K20, 35J75

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-40-111, author = {Jin , Tianling and Xiong , Jingang}, title = {Hölder Regularity for the Linearized Porous Medium Equation in Bounded Domains}, journal = {Analysis in Theory and Applications}, year = {2024}, volume = {40}, number = {2}, pages = {111--171}, abstract = {

In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the linearized fast diffusion equation and the linearized porous medium equation with the homogeneous Dirichlet boundary condition. We prove the Hölder regularity of their weak solutions.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2023-0015}, url = {http://global-sci.org/intro/article_detail/ata/23232.html} }
TY - JOUR T1 - Hölder Regularity for the Linearized Porous Medium Equation in Bounded Domains AU - Jin , Tianling AU - Xiong , Jingang JO - Analysis in Theory and Applications VL - 2 SP - 111 EP - 171 PY - 2024 DA - 2024/07 SN - 40 DO - http://doi.org/10.4208/ata.OA-2023-0015 UR - https://global-sci.org/intro/article_detail/ata/23232.html KW - Singular parabolic equations, degenerate parabolic equations, regularity, porous medium equations. AB -

In this paper, we systematically study weak solutions of a linear singular or degenerate parabolic equation in a mixed divergence form and nondivergence form, which arises from the linearized fast diffusion equation and the linearized porous medium equation with the homogeneous Dirichlet boundary condition. We prove the Hölder regularity of their weak solutions.

Tianling Jin & Jingang Xiong. (2024). Hölder Regularity for the Linearized Porous Medium Equation in Bounded Domains. Analysis in Theory and Applications. 40 (2). 111-171. doi:10.4208/ata.OA-2023-0015
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