کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
844378 908587 2007 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Wiener’s criterion for the unique solvability of the Dirichlet problem in arbitrary open sets with non-compact boundaries
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Wiener’s criterion for the unique solvability of the Dirichlet problem in arbitrary open sets with non-compact boundaries
چکیده انگلیسی

This paper establishes a necessary and sufficient condition for the existence of a unique bounded solution to the classical Dirichlet problem in arbitrary open subset of RNRN (N≥3N≥3) with a non-compact boundary. The criterion is the exact analogue of Wiener’s test for the boundary regularity of harmonic functions and characterizes the “thinness” of a complementary set at infinity. The Kelvin transformation counterpart of the result reveals that the classical Wiener criterion for the boundary point is a necessary and sufficient condition for the unique solvability of the Dirichlet problem in a bounded open set within the class of harmonic functions having a “fundamental solution” kind of singularity at the fixed boundary point. Another important outcome is that the classical Wiener’s test at the boundary point presents a necessary and sufficient condition for the “fundamental solution” kinds of singularities of the solution to the Dirichlet problem to be removable.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 67, Issue 2, 15 July 2007, Pages 563–578
نویسندگان
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