See MathJax.Hub.Config({ tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]} }); Piotr Hajlasz
Publications of Piotr Hajlasz

2019 and later

[1] P. Goldstein, P. Hajlasz, Jacobians of $W^{1,p}$ homeomorphisms, case $p=[n/2]$ (Submitted). arXiv
[2] P. Hajlasz, S. Zimmerman, An implicit function theorem for Lipschitz mappings into metric spaces (Submitted). arXiv
[3] P. Goldstein, P. Hajlasz, Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion. Ann. Mat. Pura Appl. (Available online). arXiv
[4] P. Goldstein, P. Hajlasz, P. Pankka, Topologically nontrivial counterexamples to Sard's theorem Int. Mat. Res. Not. IMRN. (Available online). arXiv
[5] P. Goldstein, P. Hajlasz, M. R. Pakzad, Finite distortion Sobolev mappings between manifolds are continuous. Int. Math. Res. Not. IMRN. (Available online). arXiv

2018

[6] P. Hajlasz, S. Malekzadeh, S. Zimmerman, Weak BLD mappings and Hausdorff measure. Nonlinear Analysis. 177 (2018), 524-531. arXiv
[7] P. Goldstein, P. Hajlasz, $C^1$ mappings in $R^5$ with derivative of rank at most 3 cannot be uniformly approximated by $C^2$ mappings with derivative of rank at most 3 J. Math. Anal. Appl. 468 (2018), 1108-1114. arXiv
[8] P. Goldstein, P. Hajlasz, Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian. Ann. Acad. Sci. Fenn. Math. 43 (2018), 147-170. arXiv
[9] P. Hajlasz, The (n+1)-Lipschitz homotopy group of the Heisenberg group Hn. Proc. Amer. Math. Soc. 146 (2018), 1305-1308. arXiv

2017

[10] P. Hajlasz, S. Zimmerman, Dubovitskij-Sard theorem for Sobolev mappings. Indiana Univ. Math. J. 66 (2017), 705-723. arXiv
[11] P. Goldstein, P. Hajlasz, A measure and orientation preserving homeomorphism of a cube with Jacobian equal $-1$ almost everywhere. Arch. Ration. Mech. Anal. 225 (2017), 65-88. arXiv
[12] P. Hajlasz, Z. Liu, A Marcinkiewicz integral type characterization of the Sobolev space. Publ. Mat. Publ. Mat. 61 (2017), 83--104. arXiv
[13] P. Hajlasz, M. V. Korobkov, J. Kristensen. A bridge between Dubovitskii-Federer theorems and the coarea formula J. Funct. Anal. 272 (2017), 1265-1295. arXiv

2016

[14] P. Hajlasz, X. Zhou, Sobolev homeomorphism on a sphere containing an arbitrary Cantor set in the image. Geom. Dedicata 184 (2016), 159-173. arXiv

2015

[15] P. Hajlasz, S. Malekzadeh, A new characterization of the mappings of bounded length distortion. Int. Math. Res. Not. IMRN 2015, no. 24, 13238-13244. arXiv
[16] P. Hajlasz, S. Zimmerman, Geodesics in the Heisenberg group. Anal. Geom. Metr. Spaces 3 (2015), 325-337. arXiv
[17] P. Hajlasz, S. Malekzadeh, On conditions for unrectifiability of a metric space. Anal. Geom. Metr. Spaces 3 (2015), 1-14. arXiv

2014

[18] Z. M. Balogh, P. Hajlasz, K. Wildrick, Weak contact equations for mappings into Heisenberg groups. Indiana Univ. Math. J. 63 (2014), 1839-1873. arXiv
[19] P. Hajlasz, Z. Liu, Maximal potentials, maximal singular integrals and the spherical maximal function. Proc. Amer. Math. Soc. 142 (2014), 3965-3974. arXiv
[20] P. Hajlasz, A. Schikorra, Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 39 (2014), 593-604. arXiv
[21] N. DeJarnette, P. Hajlasz, A. Lukyanenko, J. Tyson, On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target. Conform. Geom. Dyn. 18 (2014), 119-156. arXiv
[22] P. Hajlasz, A. Schikorra, J. Tyson, Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups Geom. Funct. Anal. 24 (2014), 245-268 arXiv

2013

[23] P. Hajlasz, Z. Liu, Sobolev spaces, Lebesgue points and maximal functions J. Fixed Point Theory Appl. 13 (2013), 259-269. arXiv
[24] P. Hajlasz, J. Mirra, The Lusin theorem and horizontal graphs in the Heisenberg group Anal. Geom. Metr. Spaces 1 (2013), 295-301. pdf
[25] J. Gong, P. Hajlasz, Differentiability of p-harmonic functions on metric measure spaces. Potential Analysis 38 (2013), 79-93. pdf

2012

[26] P. Goldstein, P. Hajlasz, Sobolev mappings, degree, homotopy classes and rational homology spheres. J. Geom. Anal. 22 (2012), 320-338. pdf

2011

[27] P. Hajlasz, Sobolev mappings: Lipschitz density is not an isometric invariant of the target. Int. Math. Res. Not. IMRN Vol. 2011, no.12, 2794-2809. pdf

2010

[28] P. Hajlasz, Z. Liu, A compact emebdding of a Sobolev space is equivalent to an emebdding into a better space. Proc. Amer. Math. Soc. 138 (2010), 3257-3266. pdf
[29] P. Hajlasz, J. Maly, On approximate differentiability of the maximal function. Proc. Amer. Math. Society. 138 (2010), 165--174.
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2009

[30] P. Hajlasz, Density of Lipschitz mappings in the class of Sobolev mappings between metric spaces. Math. Ann. 343 (2009), 801-823. pdf
[31] P. Hajlasz, Sobolev mappings between manifolds and metric spaces. In: Sobolev Spaces in Mathematics I. Sobolev type Inequalities pp. 185-222. International Mathematical Series. Springer 2009.
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2008

[32] P. Hajlasz, J. Tyson, Sobolev Peano cubes. Michigan Math. J. 56 (2008), 687-702.pdf
[33] P. Hajlasz, P. Strzelecki, X. Zhong, A new approach to interior regularity of elliptic systems with quadratic Jacobain structure in dimention two. Manuscripta Math. 127 (2008), 121-135.
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[34] P. Hajlasz, P. Koskela, H. Tuominen, Measure density and extendability of Sobolev functions Rev. Mat. Iberoamericana 24 (2008), 645-669.
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[35] P. Hajlasz, P. Koskela, H. Tuominen, Sobolev embeddings, extensions and measure density condition J. Funct. Anal. 254 (2008), 1217--1234.
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[36] P. Hajlasz, T. Iwaniec, J. Maly, J. Onninen, Weakly differentiable mappings between manifolds. Memoirs Amer. Math. Soc. 899 (2008), 1--72.
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2007

[37] P. Hajlasz, Sobolev mappings: Lipschitz density is not a bi-Lipschitz invariant of the target. Geom. Funct. Anal. 17 (2007), 435-467. pdf

2005

[38] B. Bojarski, P. Hajlasz, P. Strzelecki, Sard's theorem for mappings in Holder and Sobolev spaces. Manuscripta Math. 118 (2005), 383-397 pdf
[39] P. Hajlasz, P. Strzelecki, How to measure volume with a thread. Amer. Math. Monthly 112 (2005), 176-179.
pdf Read also Erratum

2004

[40] P. Hajlasz, P. Koskela, Formation of cracks under deformations with finite energy. Calc. Var. Partial Differential Equations 19 (2004), 221--227.pdf
[41] P. Hajlasz, J. Onninen, On boundedness of maximal functions in Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 29 (2004), no. 1, 167--176.
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2003

[42] P. Hajlasz, Whitney's example by way of Assouad's embedding. Proc. Amer. Math. Soc. 131 (2003), 3463--3467 pdf
[43] P. Hajlasz, A new characterization of the Sobolev space. (Dedicated to Professor Aleksander Pelczynski on the occasion of his 70th birthday.) Studia Math. 159 (2003), 263--275.
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[44] P. Hajlasz, Sobolev spaces on metric-measure spaces. (Heat kernels and analysis on manifolds, graphs, and metric spaces (Paris, 2002)), 173--218, Contemp. Math. , 338, Amer. Math. Soc., Providence, RI, 2003.
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2002

[45] P. Hajlasz, J. Maly, Approximation in Sobolev spaces of nonlinear expressions involving the gradient Ark. Mat. 40 (2002), 245--274.pdf
[46] B. Bojarski, P. Hajlasz, P. Strzelecki, Improved $C^{k,\lambda}$ approximation of higher order Sobolev functions in norm and capacity. Indiana Univ. Mat. J. 51 (2002), 507--540.
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2001

[47] P. Hajlasz, Sobolev inequalities, truncation method, and John domains. (Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday.) Report. Univ. Jyvaskyla 83 (2001), 109--126.pdf

2000

[48] P. Hajlasz, P. Koskela, Sobolev met Poincare, Memoirs Amer. Math. Soc. 688 (2000), 1--101. pdf
[49] B. Franchi, P. Hajlasz, How to get rid of one of the weights in a two weight Poincare inequality?, Ann. Polon. Math 74 (2000), 97--103.
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[50] P. Hajlasz, Sobolev mappings, co-area fromula and related topics. In: Proceedings on Analysis and Geometry. Novosibirsk: Sobolev Instinute Press, 2000, pp. 227--254.
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1999

[51] P. Hajlasz, Pointwise Hardy inequalities Proc. Amer. Math. Soc. 127(1999), 417--423. pdf
[52] B. Franchi, P. Hajlasz, P. Koskela, Definitions of Sobolev classes on metric spaces, Ann. Inst. Fourier (Grenoble) 49 (1999), 1903--1924.
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1998

[53] P. Hajlasz, P. Strzelecki, Subelliptic p-harmonic maps into spheres and the ghost of Hardy spaces, Math. Ann. 312 (1998), 341--362. pdf
[54] P. Hajlasz, P. Koskela, Isoperimetric inequalities and imbedding theorems in irregular domains, J. London Math. Soc. 58 (1998), 425-450.
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[55] P. Hajlasz, J. Kinnunen, Holder quasicontinuity of Sobolev functions on metric spaces Rev. Mat. Iberoamericana, 14 (1998), 601--622.
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1997

[56] P.Hajlasz, O. Martio, Traces of Sobolev functions on fractal type sets and characterization of extension domains J. Funct. Anal., 143(1997), 221--246. pdf

1996

[57] P. Hajlasz, Sobolev spaces on an arbitrary metric space, Potential Analysis , 5 (1996), 403--415. pdf
[58] P. Hajlasz, A counterexample to the $L^p$--Hodge decomposition, Banach Center Publications 33 (1996), 79--83.
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[59] P. Hajlasz, On approximate differentiability of functions with bounded deformation Manuscripta Math. 91 (1996), 61--72.
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1995

[60] P. Hajlasz, P. Koskela, Sobolev meets Poincare, C. R. Acad Sci. Paris 320 (1995), 1211--1215. pdf
[61] P. Hajlasz, Boundary behaviour of Sobolev mappings, Proc. Amer. Math. Soc. , 123 (1995), 1145--1148.
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[62] P. Hajlasz, A note on weak approximation of minors, Ann. I. H. P. Analyse non lineaire, 12 (1995), 415--424.
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[63] P. Hajlasz, Geometric approach to Sobolev spaces and badly degenerate elliptic equations, GAKUTO International Series; Mathematical Sciences and Applications, vol. 7, (1995) pp. 141--168. Nonlinear Analysis and Applications (The Proceedings of Banach Center Minisemester, November-Decembed, 1994) N.Kenmochi, M. Niezgodka, P. Strzelecki eds.
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[64] P. Hajlasz, A. Kalamajska, Polynomial asymptotics and approximation of Sobolev functions, Studia Math. 113(1995), 55--64.
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1994

[65] P. Hajlasz, Equivalent statement of the Poincare conjecture, Annali. Mat. Pura Appl. 167 (1994), 25--31. pdf
[66] P. Hajlasz, Approximation of Sobolev mappings, Nonlinear Analysis 22 (1994), 1579-1591.
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[67] P. Hajlasz, A Sard type theorem for Borel mappings, Colloq. Math. 67 (1994), 217--221.
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1993

[68] B. Bojarski, P. Hajlasz, Pointwise inequalities for Sobolev functions and some applications. Studia Math. 106 (1993), 77--92.pdf
[69] P. Hajlasz, Change of variables formula under minimal assumptions. Colloq. Math. 64 (1993), 93--101.
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[70] P. Hajlasz, Note on Meyers--Serrin's Theorem. Expositiones Math. 11 (1993), 377--379.
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[71] P. Hajlasz, P. Strzelecki, On the differentiability of solutions of quasilinear elliptic equations, Colloq. Math. 64 (1993), 287--291.
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