W. Górny and J.M. Mazón, Functions of Least Gradient, Monographs in Mathematics, vol. 110, 2024, ISBN 978-3-031-51880-5. DOI: 10.1007/978-3-031-51881-2.
Journal articles
W. Górny, P. Rybka and A. Sabra, Special cases of the planar least gradient problem, Nonlinear Anal. 151 (2017), pp. 66-95. DOI: 10.1016/j.na.2016.11.020.
W. Górny, Planar least gradient problem: existence, regularity and anisotropic case, Calc. Var. Partial Differential Equations 57, no. 4 (2018), Art. 98. DOI: 10.1007/s00526-018-1378-y.
W. Górny, (Non)uniqueness of minimizers in the least gradient problem, J. Math. Anal. Appl. 468 (2018), pp. 913-938. DOI: 10.1016/j.jmaa.2018.08.038.
W. Górny, Lp regularity of least gradient functions, Proc. Amer. Math. Soc. 148 (7) (2020), pp. 3009-3019. DOI: 10.1090/proc/15031.
W. Górny, Least gradient problem with respect to a non-strictly convex norm, Nonlinear Anal. 200 (2020), 112049. DOI: 10.1016/j.na.2020.112049.
W. Górny and J.M. Mazón, Least gradient functions in metric random walk spaces, ESAIM:COCV 27 (2021), S28. DOI: 10.1051/cocv/2020087.
W. Górny, Existence of minimisers in the least gradient problem for general boundary data, Indiana Univ. Math. J. 70, no. 3 (2021), pp. 1003-1037. DOI: 10.1512/iumj.2021.70.8420.
W. Górny, Bourgain-Brezis-Mironescu approach in metric spaces with Euclidean tangents, J. Geom. Anal. 32 (4) (2022), Art. 128. DOI: 10.1007/s12220-021-00861-4.
W. Górny, Local and nonlocal 1-Laplacian in Carnot groups, Ann. Fenn. Math. 47 (1) (2022), pp. 427-456. DOI: 10.54330/afm.114742.
S. Dweik and W. Górny, Least gradient problem on annuli, Analysis & PDE 15 (3) (2022), pp. 699-725. DOI: 10.2140/apde.2022.15.699.
W. Górny and J.M. Mazón, On the p-Laplacian evolution equation in metric measure spaces, J. Funct. Anal. 283 (2022), 109621. DOI: 10.1016/j.jfa.2022.109621.
W. Górny, The trace space of anisotropic least gradient functions depends on the anisotropy, Math. Ann. 387 (2023), 1343–1365. DOI: 10.1007/s00208-022-02488-4.
S. Dweik and W. Górny, Optimal transport approach to Sobolev regularity of solutions to the weighted least gradient problem, SIAM. J. Math. Anal. 55 (2023), no. 3, pp. 1916-1948. DOI: 10.1137/21M1468358.
W. Górny, Applications of optimal transport methods in the least gradient problem, Ann. Scu. Norm. Sup. Pisa Cl. Sci. (5) 24 (2023), pp. 1817-1851. DOI: 10.2422/2036-2145.202105_049.
W. Górny and J.M. Mazón, The Neumann and Dirichlet problems for the total variation flow in metric measure spaces, Adv. Calc. Var. 17 (2024), 131-164. DOI: 10.1515/acv-2021-0107.
W. Górny and J.M. Mazón, The Anzellotti-Gauss-Green formula and least gradient functions in metric measure spaces, Commun. Contemp. Math. 26 (2024), no. 6, 2350027. DOI: 10.1142/S021919972350027X.
M. Friedrich, W. Górny and U. Stefanelli, The double-bubble problem on the square lattice, Interfaces Free Bound. 26 (2024), no. 1, pp. 79-134. DOI: 10.4171/ifb/510.
W. Górny, Least gradient problem with Dirichlet condition imposed on a part of the boundary, Calc. Var. Partial Differential Equations 63 (2024), Art. 58. DOI: 10.1007/s00526-023-02646-9.
W. Górny and J.M. Mazón, A duality-based approach to gradient flows of linear growth functionals, Publ. Mat., to appear (preprint available at arXiv:2212.08725).
Conference proceedings
W. Górny and J.M. Mazón, Weak solutions to gradient flows in metric measure spaces, Proc. Appl. Math. Mech. 22:1 (2022), e202200099. DOI: 10.1002/pamm.202200099.
W. Górny and J.M. Mazón, Weak solutions to the total variation flow in metric measure spaces, in: Ferreira et al. (eds.), Proceedings book. XXVII Congreso de Ecuaciones Diferenciales y XVII Congreso de Matemática Aplicada, Zaragoza, July 18th–22nd, 2022. Prensas de la Universidad de Zaragoza, pp. 55--62, 2023. DOI: 10.26754/uz.978-84-18321-66-5.
Preprints
W. Górny, Strongly anisotropic Anzellotti pairings and their applications to the anisotropic p-Laplacian, preprint (2023), available at arXiv:2305.18876.
W. Górny, Weak solutions to gradient flows of functionals with inhomogeneous growth in metric spaces, preprint (2023), available at arXiv:2307.13456.
M. Friedrich, W. Górny and U. Stefanelli, A characterization of l1 double bubbles with general interface interaction, preprint (2023), available at arXiv:2311.07782.
S. Buccheri and W. Górny, A metric counterpart of the Gu-Yung formula, preprint (2024), available at arXiv:2403.13475.
M. Friedrich, W. Górny and U. Stefanelli, The l1 double-bubble problem in three dimensions, preprint (2024), available at arXiv:2403.19295.
W. Górny, J.M. Mazón, J. Toledo, Evolution problems with perturbed 1-Laplacian type operators on random walk spaces, preprint (2024), available at arXiv:2410.15203.