TY - JOUR A1 - Dancer, E.N. A1 - Daners, Daniel A1 - Hauer, Daniel T1 - Uniform convergence of solutions to elliptic equations on domains with shrinking holes JF - Advances in Differential Equations Y1 - 2015 U6 - https://doi.org/10.57262/ade/1427744013 SN - 1079-9389 VL - 20 IS - 5/6 SP - 463 EP - 494 PB - Khayyam Publishing, Inc ER - TY - JOUR A1 - Hauer, Daniel A1 - He, Yuhan A1 - Liu, Dehui T1 - Fractional Powers of Monotone Operators in Hilbert Spaces JF - Advanced Nonlinear Studies N2 - The aim of this article is to provide a functional analytical framework for defining the fractional powers As for −1 < s < 1 of maximal monotone (possibly multivalued and nonlinear) operators A in Hilbert spaces.We investigate the semigroup {e−As t}t≥0 generated by −As, prove comparison principles and interpolations properties of {e−As t}t≥0 in Lebesgue and Orlicz spaces. We give sufficient conditions implying that As has a sub-differential structure. These results extend earlier ones obtained in the case s = 1/2 for maximal monotone operators [H. Brézis, Équations d’évolution du second ordre associées à des opérateurs monotones, Israel J. Math. 12 (1972), 51–60], [V. Barbu, A class of boundary problems for second order abstract differential equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 19 (1972), 295–319], [V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff international, Leiden, 1976], [E. I. Poffald and S. Reich, An incomplete Cauchy problem, J. Math. Anal. Appl. 113 (1986), no. 2, 514–543], and the recent advances for linear operators A obtained in [L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32 (2007), no. 7–9, 1245–1260], [P. R. Stinga and J. L. Torrea, Extension problem and Harnack’s inequality for some fractional operators, Comm. Partial Differential Equations 35 (2010), no. 11, 2092–2122]. Y1 - 2019 U6 - https://doi.org/10.1515/ans-2019-2053 SN - 1536-1365 VL - 19 IS - 4 SP - 717 EP - 755 PB - Walter de Gruyter GmbH ER - TY - JOUR A1 - Hauer, Daniel A1 - Mazón, José M. T1 - Kurdyka–Łojasiewicz–Simon inequality for gradient flows in metric spaces JF - Transactions of the American Mathematical Society Y1 - 2019 U6 - https://doi.org/10.1090/tran/7801 SN - 0002-9947 VL - 372 IS - 7 SP - 4917 EP - 4976 PB - American Mathematical Society (AMS) ER - TY - JOUR A1 - Chill, Ralph A1 - Hauer, Daniel A1 - Kennedy, James T1 - Nonlinear semigroups generated by j-elliptic functionals JF - Journal de Mathématiques Pures et Appliquées Y1 - 2016 U6 - https://doi.org/10.1016/j.matpur.2015.11.005 SN - 0021-7824 VL - 105 IS - 3 SP - 415 EP - 450 PB - Elsevier BV ER - TY - JOUR A1 - Goldstein, Jerome A. A1 - Hauer, Daniel A1 - Rhandi, Abdelaziz T1 - Existence and nonexistence of positive solutions of p-Kolmogorov equations perturbed by a Hardy potential JF - Nonlinear Analysis Y1 - 2016 U6 - https://doi.org/10.1016/j.na.2015.07.016 SN - 0362-546X VL - 131 SP - 121 EP - 154 PB - Elsevier BV ER - TY - JOUR A1 - Hauer, Daniel T1 - The p-Dirichlet-to-Neumann operator with applications to elliptic and parabolic problems JF - Journal of Differential Equations Y1 - 2015 U6 - https://doi.org/10.1016/j.jde.2015.04.030 SN - 0022-0396 VL - 259 IS - 8 SP - 3615 EP - 3655 PB - Elsevier BV ER - TY - GEN A1 - Hauer, Daniel T1 - Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval: the singular case T2 - Nonlinear Differential Equations and Applications NoDEA Y1 - 2013 U6 - https://doi.org/10.1007/s00030-012-0203-0 SN - 1021-9722 VL - 20 (2013) IS - 3 SP - 1171 EP - 1190 PB - Springer Science and Business Media LLC ER - TY - GEN A1 - Collier, Timothy Allen A1 - Hauer, Daniel T1 - A density result for doubly nonlinear operators in L1 T2 - Discrete and Continuous Dynamical Systems - S Y1 - 2024 U6 - https://doi.org/10.3934/dcdss.2024031 SN - 1937-1632 VL - 17 IS - 4 SP - 1663 EP - 1671 PB - American Institute of Mathematical Sciences (AIMS) ER - TY - GEN A1 - Gurka, Petr A1 - Hauer, Daniel T1 - More insights into the Trudinger–Moser inequality with monomial weight T2 - Calculus of Variations and Partial Differential Equations Y1 - 2021 U6 - https://doi.org/10.1007/s00526-020-01890-7 SN - 0944-2669 VL - 60 PB - Springer Science and Business Media LLC ER - TY - GEN A1 - Hauer, Daniel T1 - Regularizing effect of homogeneous evolution equations with perturbation T2 - Nonlinear Analysis Y1 - 2021 U6 - https://doi.org/10.1016/j.na.2021.112245 SN - 0362-546X VL - 206 PB - Elsevier BV ER - TY - GEN A1 - Andrews, Ben A1 - Clutterbuck, Julie A1 - Hauer, Daniel T1 - The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions T2 - Proceedings of the American Mathematical Society Y1 - 2021 U6 - https://doi.org/10.1090/proc/15140 SN - 0002-9939 VL - 149 IS - 4 SP - 1481 EP - 1493 PB - American Mathematical Society (AMS) ER - TY - GEN A1 - Andrews, Ben A1 - Clutterbuck, Julie A1 - Hauer, Daniel T1 - Non-concavity of the Robin ground state T2 - Cambridge Journal of Mathematics Y1 - 2020 U6 - https://doi.org/10.4310/cjm.2020.v8.n2.a1 SN - 2168-0930 VL - 8 IS - 2 SP - 243 EP - 310 PB - International Press of Boston ER - TY - GEN A1 - Arendt, Wolfgang A1 - Hauer, Daniel T1 - Maximal L2-regularity in nonlinear gradientsystems and perturbations of sublinear growth T2 - Pure and Applied Analysis Y1 - 2020 U6 - https://doi.org/10.2140/paa.2020.2.23 SN - 2578-5885 VL - 2 IS - 1 SP - 23 EP - 34 PB - Mathematical Sciences Publishers ER - TY - JOUR A1 - Hauer, Daniel A1 - Mazón, José M. T1 - Regularizing effects of homogeneous evolution equations: the case of homogeneity order zero JF - Journal of Evolution Equations Y1 - 2019 U6 - https://doi.org/10.1007/s00028-019-00502-y SN - 1424-3199 VL - 19 IS - 4 SP - 965 EP - 996 PB - Springer Science and Business Media LLC ER -