Abstract
We prove the Hölder continuity of a homeomorphism f defined on a bounded
domain
Funding statement: The research was supported by the Ministry of Science, Serbia, project OI 174017.
References
[1] L. V. Ahlfors, Lectures on Quasiconformal Mappings, 2nd ed., Univ. Lecture Ser. 38, American Mathematical Society, Providence, 2006. 10.1090/ulect/038Search in Google Scholar
[2] A. P. Calderon, On the differentiability of absolutely continuous functions, Riv. Mat. Univ. Parma 2 (1951), 203–213. Search in Google Scholar
[3] L. D’Onofrio, Differentiability versus approximate differentiability, Proceedings of the International Conference “Two nonlinear days in Urbino 2017”, Electron. J. Differ. Equ. Conf. 25, Texas State Univérsity, San Marcos (2018), 77–85. Search in Google Scholar
[4]
L. D’Onofrio, S. Hencl, J. Malý and R. Schiattarella,
Note on Lusin
[5] L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions, Stud. Adv. Math., CRC Press, Boca Raton, 1992. Search in Google Scholar
[6] H. Federer, Geometric Measure Theory, Grundlehren Math. Wiss. 153, Springer, New York, 1969. Search in Google Scholar
[7] D. Kovtonyuk and V. Ryazanov, New modulus estimates in Orlicz–Sobolev classes, Ann. Univ. Buchar. Math. Ser. 5 (2014), no. 1, 131–135. Search in Google Scholar
[8] D. Kovtonyuk, V. Ryazanov, R. Salimov and E. Sevost’yanov, On the theory of Orlicz–Sobolev classes (in Russian), Algebra i Analiz 25 (2013), no. 6, 50–102; translation in St. Petersburg Math. J. 25 (2014), no. 6, 929–963. Search in Google Scholar
[9] M. Mateljević, R. Salimov and E. Sevostyanov, Hölder and Lipschitz continuity of mappings in Orlicz–Sobolev classes with the distortion of bounded mean value type and harmonic mappings, preprint (2022), http://arxiv.org/abs/2208.02551. Search in Google Scholar
[10] V. Mazya, Sobolev Spaces with Applications to Elliptic Partial Differential Equations, Grundlehren Math. Wiss. 342, Springer, Heidelberg, 2011. 10.1007/978-3-642-15564-2Search in Google Scholar
[11] E. A. Sevost’yanov, On the boundary behavior of open discrete mappings with unbounded characteristic, Ukrainian Math. J. 64 (2012), no. 6, 979–984. 10.1007/s11253-012-0693-2Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- On the Hölder continuity of ring Q-homeomorphisms
- New regularity results for the heat equation and application to non-homogeneous Burgers equation
- Maximum inequalities in rearrangements of orthogonal series
- A parallel type decomposition scheme for quasi-linear abstract hyperbolic equation
- Reversible ring property via idempotent elements
- Infinitely many solutions for perturbed Λγ-Laplace equations
- On an alternative approach for mixed boundary value problems for the Laplace equation
- Split monotone variational inclusion problem involving Cayley operators
- Duals and approximate duals of von Neumann–Schatten p-frames
- Properties of general Fourier coefficients of differentiable functions
- On linear spline algorithms of computerized tomography in the space of n-orbits
- Barbashin type characterizations for the uniform polynomial stability and instability of evolution families
Articles in the same Issue
- Frontmatter
- On the Hölder continuity of ring Q-homeomorphisms
- New regularity results for the heat equation and application to non-homogeneous Burgers equation
- Maximum inequalities in rearrangements of orthogonal series
- A parallel type decomposition scheme for quasi-linear abstract hyperbolic equation
- Reversible ring property via idempotent elements
- Infinitely many solutions for perturbed Λγ-Laplace equations
- On an alternative approach for mixed boundary value problems for the Laplace equation
- Split monotone variational inclusion problem involving Cayley operators
- Duals and approximate duals of von Neumann–Schatten p-frames
- Properties of general Fourier coefficients of differentiable functions
- On linear spline algorithms of computerized tomography in the space of n-orbits
- Barbashin type characterizations for the uniform polynomial stability and instability of evolution families