| 1. |
- Adamowicz, Tomasz, et al.
(författare)
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Prime ends for domains in metric spaces
- 2013
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Ingår i: Advances in Mathematics. - : Elsevier. - 0001-8708 .- 1090-2082. ; 238, s. 459-505
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Caratheodory and Nakki. Modulus ends and prime ends, defined by means of the p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.
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| 2. |
- Adamowicz, Tomasz, et al.
(författare)
-
Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points
- 2014
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Ingår i: Annales de l'Institut Henri Poincare. Analyse non linéar. - : Elsevier Masson / Institute Henri Poincar�. - 0294-1449 .- 1873-1430. ; 31:6, s. 1131-1153
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Tidskriftsartikel (refereegranskat)abstract
- We study various boundary and inner regularity questions for p(.)-(super)harmonic functions in Euclidean domains. In particular, we prove the Kellogg property and introduce a classification of boundary points for p(.)-harmonic functions into three disjoint classes: regular, semiregular and strongly irregular points. Regular and especially semiregular points are characterized in many ways. The discussion is illustrated by examples. Along the way, we present a removability result for bounded p(.)-harmonic functions and give some new characterizations of W-0(1,p(.)) spaces. We also show that p(.)-superharmonic functions are lower semicontinuously regularized, and characterize them in terms of lower semicontinuously regularized supersolutions.
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| 3. |
- Adamowicz, Tomasz, et al.
(författare)
-
The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures
- 2016
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Ingår i: Annali di Matematica Pura ed Applicata. - : Springer. - 0373-3114 .- 1618-1891. ; 195:2, s. 623-658
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Tidskriftsartikel (refereegranskat)abstract
- We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.
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