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• W4387311611 abstract "Abstract We establish pointwise bounds expressed in terms of a nonlinear potential of a generalized Wolff type for <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=script>𝒜</m:mi> </m:math> {{mathcal{A}}} -superharmonic functions with nonlinear operator <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mi mathvariant=script>𝒜</m:mi> <m:mo>:</m:mo> <m:mrow> <m:mrow> <m:mi mathvariant=normal>Ω</m:mi> <m:mo>×</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> <m:mo>→</m:mo> <m:msup> <m:mi>ℝ</m:mi> <m:mi>n</m:mi> </m:msup> </m:mrow> </m:mrow> </m:math> {{mathcal{A}}:Omegatimes{mathbb{R}^{n}}to{mathbb{R}^{n}}} having measurable dependence on the spacial variable and Orlicz growth with respect to the last variable. The result is sharp as the same potential controls estimates from above and from below. Applying it we provide a bunch of precise regularity results including continuity and Hölder continuity for solutions to problems involving measures that satisfy conditions expressed in the natural scales. Finally, we give a variant of Hedberg–Wolff theorem on characterization of the dual of the Orlicz space." @default.
• W4387311611 created "2023-10-04" @default.
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• W4387311611 date "2023-10-04" @default.
• W4387311611 modified "2023-10-05" @default.
• W4387311611 title "Wolff potentials and local behavior of solutions to elliptic problems with Orlicz growth and measure data" @default.
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• W4387311611 doi "https://doi.org/10.1515/acv-2023-0005" @default.
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