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Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations
Thomas Runst,Winfried Sickel +1 more
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The article was published on 1996-01-01 and is currently open access. It has received 1121 citations till now. The article focuses on the topics: Sobolev inequality & Domain (mathematical analysis).read more
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Hitchhiker's guide to the fractional Sobolev spaces
TL;DR: In this article, the authors deal with the fractional Sobolev spaces W s;p and analyze the relations among some of their possible denitions and their role in the trace theory.
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Hitchhiker's guide to the fractional Sobolev spaces
TL;DR: In this article, the authors deal with the fractional Sobolev spaces W^[s,p] and analyze the relations among some of their possible definitions and their role in the trace theory.
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A few remarks on the Camassa-Holm equation
TL;DR: In this paper, the existence and uniqueness of solutions for the Camassa-Holm equation with minimal regularity assumptions on the initial data were proved. But the existence time of these solutions is not known.
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Bounded Minimisers of Double Phase Variational Integrals
Maria Colombo,Giuseppe Mingione +1 more
TL;DR: Bounded minimisers of the functional functional minimization problem were studied in this article, where the sharp bound was shown to hold for the case where p < q and 1 < q.
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The Calderón-Zygmund theory for elliptic problems with measure data
TL;DR: In this paper, the authors consider non-linear elliptic equations having a measure in the right hand side, of the type div a(x, Du) = μ, and prove differentiability and integrability results for solutions.