Sobolev’s inequality for double phase functionals with variable exponents
AbstractOur aim in this paper is to establish generalizations of Sobolev’s inequality for double phase functionals {\Phi(x,t)=t^{p(x)}+a(x)t^{q(x)}}, where {p(\,{\cdot}\,)} and {q(\,{\cdot}\,)} satisfy log-Hölder conditions and {a(\,{\cdot}\,)} is nonnegative, bounded and Hölder continuous of order {\theta\in(0,1]}.
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2019 ◽
Vol 9
(1)
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pp. 710-728
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2019 ◽
Vol 63
(2)
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pp. 304-317
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2020 ◽
Vol 59
(5)
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