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Gradient estimates for double phase problems with two modulating coefficients
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DOI：10.1007/s00030-025-01162-3.png)
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Abstract
En 中文
In this paper, we consider a class of non-uniformly elliptic equations whose model is given by -div(a(x)|Du|(p-2)Du+b(x)|Du|(q-2)Du) =-div(a(x)|F|Fp-2+b(x)|F|Fq-2), where 1 ),b()>= 0 and 0<= a()+b(). Here, the modulating coefficient b() is assumed to be H older continuous and the modulating coefficient a() is assumed to be uniformly continuous. We prove the following regularity result with non-standard growth conditions:(a(x)|F|(p)+b(x)|F|(q))is an element of L-loc(gamma)=double right arrow(a(x)|Du|(p)+b(x)|Du|(q))is an element of L-loc(gamma),for all gamma >= 1, and establish the corresponding gradient estimates.
Keywords:
Double phase problems
Gradient estimates
Modulating coefficients
Nonstandard growth
Nonuniform ellipticity
Journal
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1.2
Papers:
91
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