کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4665317 1633801 2016 110 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On planar Sobolev Lpm-extension domains
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On planar Sobolev Lpm-extension domains
چکیده انگلیسی

For each m≥1m≥1 and p>2p>2 we characterize bounded simply connected Sobolev Lpm-extension domains Ω⊂R2Ω⊂R2. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in Ω. Its proof is based on a series of results related to the existence of special chains of squares joining given points x and y in Ω.An important geometrical ingredient for obtaining these results is a new “Square Separation Theorem”. It states that under certain natural assumptions on the relative positions of a point x   and a square S⊂ΩS⊂Ω there exists a similar square Q⊂ΩQ⊂Ω which touches S and has the property that x and S   belong to distinct connected components of Ω∖QΩ∖Q.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 287, 10 January 2016, Pages 237–346
نویسندگان
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