Boundary limits of monotone Sobolev functions on metric spaces. (English) Zbl 1477.30057
Summary: In this paper we are concerned with weighted boundary limits of monotone Sobolev functions in Orlicz spaces on bounded \((\eta,\psi)\)-John domains in a metric space. We also deal with Lindelöf type theorems for monotone Sobolev functions on uniform domains in a metric space.
MSC:
| 30L99 | Analysis on metric spaces |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
References:
| [1] | A. Björn and J. Björn: Nonlinear Potential Theory on Metric Spaces, EMS Tracts in Mathematics, 17, European Mathematical Society (EMS), Zürich, 2011. · Zbl 1231.31001 |
| [2] | L. Carleson: Selected problems on exceptional sets. Van Nostrand Mathematical Studies, No. 13 D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. · Zbl 0189.10903 |
| [3] | N. DeJarnette: Is an Orlicz-Poincaré inequality an open ended condition, and what does that mean?, J. Math. Anal. Appl 423 (2015), 358-376. · Zbl 1333.46034 |
| [4] | T. Futamura: Lindelöf theorems for monotone Sobolev functions on uniform domains, Hiroshima Math. J. 34 (2004), 413-422. · Zbl 1070.31001 |
| [5] | T. Futamura and Y. Mizuta: Lindelöf theorems for monotone Sobolev functions, Ann. Acad. Sci. Fenn. Math. 28 (2003), 271-277. · Zbl 1035.31005 |
| [6] | T. Futamura and Y. Mizuta: Boundary behavior of monotone Sobolev functions on John domains in a metric space, Complex Var. Theory Appl. 50 (2005), 441-451. · Zbl 1074.31005 |
| [7] | T. Futamura and T. Shimomura: Boundary behavior of monotone Sobolev functions in Orlicz spaces on John domains in a metric space, J. Geom. Anal. 28 (2018), 1233-1244. · Zbl 1395.30060 |
| [8] | P. Hajł asz and P. Koskela: Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000), no. 688. · Zbl 0954.46022 |
| [9] | J. Heinonen, T. Kilpeläinen and O. Martio: Nonlinear potential theory of degenerate elliptic equations, Oxford Univ. Press, New York, 1993. · Zbl 0780.31001 |
| [10] | P. Koskela, J.J. Manfredi and E. Villamor: Regularity theory and traces of \(\mathcal A\)-harmonic functions, Trans. Amer. Math. Soc. 348 (1996), 755-766. · Zbl 0849.31015 |
| [11] | H. Lebesgue: Sur le probléme de Dirichlet, Rend. Circ. Mat. Palermo 24 (1907), 371-402. · JFM 38.0392.01 |
| [12] | S. Lisini: Absolutely continuous curves in extended Wasserstein-Orlicz spaces, ESAIM: COCV. 22 (2016), 670-687. · Zbl 1348.49048 |
| [13] | J.J. Manfredi: Weakly monotone functions, J. Geom. Anal. 4 (1994), 393-402. · Zbl 0805.35013 |
| [14] | J.J. Manfredi and E. Villamor: Traces of monotone Sobolev functions, J. Geom. Anal. 6 (1996), 433-444. · Zbl 0896.31002 |
| [15] | J.J. Manfredi and E. Villamor: Traces of monotone Sobolev functions in weighted Sobolev spaces, Illinois J. Math. 45 (2001), 403-422. · Zbl 0988.30015 |
| [16] | V.G. Maz’ya and S.V. Poborichi: Differentiable functions on bad domains, World Scientific, River Edge, NJ, 1997. · Zbl 0918.46033 |
| [17] | Y. Mizuta: On the boundary limits of harmonic functions with gradient in \(L^p\), Ann. Inst. Fourier (Grenoble) 34 (1984), 99-109. · Zbl 0522.31009 |
| [18] | Y. Mizuta: On the boundary limits of harmonic functions, Hiroshima Math. J. 18 (1988), 207-217. · Zbl 0664.31007 |
| [19] | Y. Mizuta: On the existence of weighted boundary limits of harmonic functions, Ann. Inst. Fourier (Grenoble) 40 (1990), 811-833. · Zbl 0715.31002 |
| [20] | Y. Mizuta: Boundary limits of polyharmonic functions in Sobolev-Orlicz spaces, Complex Variables 27 (1995), 117-131. · Zbl 0845.31002 |
| [21] | Y. Mizuta: Tangential limits of monotone Sobolev functions, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 20 (1995), 315-326. · Zbl 0852.31008 |
| [22] | Y. Mizuta: Potential theory in Euclidean spaces, Gakkōtosho, Tokyo, 1996. · Zbl 0849.31001 |
| [23] | Y. Mizuta and T. Shimomura: Boundary limits of spherical means for BLD and monotone BLD functions in the unit ball, Ann. Acad. Sci. Fenn. Math. 24 (1999), 45-60. · Zbl 0926.31003 |
| [24] | Y. Mizuta and T. Shimomura: Differentiability and Hölder continuity of Riesz potentials of Orlicz functions, Analysis (Munich) 20 (2000), 201-223. · Zbl 0955.31002 |
| [25] | W. Orlicz: Über konjugierte Exponentenfolgen, Studia Math. 3 (1931), 200-211. · Zbl 0003.25203 |
| [26] | M.A. Ragusa and A. Tachikawa: Regularity for minimizers for functionals of double phase with variable exponents, Adv. Nonlinear Anal. 9 (2020), 710-728. · Zbl 1420.35145 |
| [27] | M.A. Ragusa, A. Tachikawa and H. Takabayashi: Partial regularity of \(p(x)\)-harmonic maps, Trans. Amer. Math. Soc. 365 (2013), 3329-3353. · Zbl 1277.35092 |
| [28] | Yu.G. Reshetnyak: Space mappings with bounded distortion, Translations of Mathematical Monographs 73, American Mathematical Society, Providence, RI, 1989. · Zbl 0667.30018 |
| [29] | J. Väisälä: Uniform domains, Tohoku Math. J. 40 (1988), 101-118. · Zbl 0627.30017 |
| [30] | E. Villamor and B.Q. Li: Boundary limits for bounded quasiregular mappings, J. Geom. Anal. 19 (2009), 708-718. · Zbl 1175.30022 |
| [31] | M. Vuorinen: Conformal geometry and quasiregular mappings, Lectures Notes in Math. 1319, Springer, Berlin-Heidelberg-New York, 1988. · Zbl 0646.30025 |
| [32] | H. Wallin: On the existence of boundary values of a class of Beppo Levi functions, Trans. Amer. Math. Soc. 120 (1965), 510-525. · Zbl 0139.06301 |
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