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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/228884
Parabolic Boundary Harnack Inequalities with Right-Hand Side
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Abstract
We prove the parabolic boundary Harnack inequality in parabolic flat Lipschitz domains by blow-up techniques, allowing, for the first time, a non-zero right-hand side. Our method allows us to treat solutions to equations driven by non-divergence form operators with bounded measurable coefficients, and a right-hand side $f \in L^q$ for $q>n+2$. In the case of the heat equation, we also show the optimal $C^{1-\varepsilon}$ regularity of the quotient. As a corollary, we obtain a new way to prove that flat Lipschitz free boundaries are $C^{1, \alpha}$ in the parabolic obstacle problem and in the parabolic Signorini problem.
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TORRES LATORRE, Clara. Parabolic Boundary Harnack Inequalities with Right-Hand Side. Archive for Rational Mechanics and Analysis. 2024. Vol. 248, num. 5. ISSN 0003-9527. [consulted: 15 of June of 2026]. Available at: https://hdl.handle.net/2445/228884