{"ID":23038727,"CreatedAt":"2026-09-17T05:30:12.286776779Z","UpdatedAt":"2026-09-17T05:30:12.286776779Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.18815","arxiv_id":"2609.18815","title":"Local behavior for solutions to inhomogeneous singular parabolic $p$-Laplace equations","abstract":"It is known that a major difficulty in proving Hölder regularity for solutions to quasilinear singular parabolic equations of $p$-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular parabolic $p$-Laplace equation with nonnegative time-independent forcing and Dirichlet data. By combining a time-rescaling argument with $L^\\infty$ comparison estimates, we derive Lipschitz regularity in time after any fixed positive elapsed time, which reduces the problem to an elliptic-type decay estimate for the spatial measure of level sets that is essentially uniform in time. This reduction enables us to address the above obstacle.","short_abstract":"It is known that a major difficulty in proving Hölder regularity for solutions to quasilinear singular parabolic equations of $p$-Laplace type via the method of intrinsic scaling is to establish the decay estimate of the space-time measure of level sets. In this paper, we consider an inhomogeneous singular parabolic $p...","url_abs":"https://arxiv.org/abs/2609.18815","url_pdf":"https://arxiv.org/pdf/2609.18815v1","authors":"[\"Xia Hao\",\"Yan Li\",\"Zhiwen Zhao\"]","published":"2026-09-16T15:22:46Z","proceeding":"math.AP","tasks":"[\"math.AP\"]","methods":"[]","has_code":false}