Global boundedness of solutions of degenerate and non-uniform parabolic equations

2025/09/27 by Dang, Thuyen, Duc, Duong Minh
#26D10 #35J08 #35J15 #35J70 #35J75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.23064

Abstract

Let 2 ≤ N∈ℕ, Ω be a bounded open in ℝ^N, T∈ (0,∞), Q=Ω× (0,T), u be a weak solution of parabolic equation (∂ u)/(∂ t) -Lu= f, where L is an elliptic operator on a space of functions on Q. The coefficients of L may not be bounded, not strictly nor uniformly elliptic, and not of Muckenhoupt type. We obtain global boundedness of u. Our result can be applied to u, which may vanish on (A× (0,T))∪ (Ω× \0\) of the boundary of Q and is free outside this set.

Citations

• Nondivergence form degenerate linear parabolic equations on the upper half space
• Nonuniformly elliptic Schauder theory
• Degenerate linear parabolic equations in divergence form on the upper half space

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