@misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {On the Morse index of minimal surfaces in R-hoch-p with polygonal boundaries}, series = {Manuscripta Mathematica}, volume = {53}, journal = {Manuscripta Mathematica}, issn = {0025-2611}, pages = {167 -- 197}, language = {en} } @misc{Mueller, author = {M{\"u}ller, Frank}, title = {The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries}, series = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze}, volume = {6}, journal = {Annali della Scuola Normale Superiore di Pisa, Classe di Scienze}, number = {4}, issn = {0391-173X}, pages = {529 -- 559}, language = {en} } @misc{Mueller, author = {M{\"u}ller, Frank}, title = {On the regularity of H-surfaces with free boundaries on a smooth support manifold}, series = {Analysis}, volume = {28}, journal = {Analysis}, number = {4}, issn = {0174-4747}, pages = {401 -- 419}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {{\"U}ber das Plateausche Problem f{\"u}r Wendelkurven}, series = {Mathematische Semesterberichte}, volume = {60}, journal = {Mathematische Semesterberichte}, number = {2}, issn = {0720-728X}, pages = {151 -- 183}, language = {de} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis : Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden}, publisher = {Springer Spektrum}, address = {Berlin [u.a.]}, isbn = {978-3-642-41506-7}, pages = {XV, 512 S.}, language = {de} } @incollection{HildebrandtSauvigny, author = {Hildebrandt, Stefan and Sauvigny, Friedrich}, title = {On Plateaus's problem in Riemannian manifolds}, series = {Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya}, booktitle = {Proceedings of the St. Petersburg mathematical society : advances in mathematical analysis of partial differential equations ; dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya}, editor = {Apushkinskaya, Darya and Nazarov, Alexander I.}, publisher = {American Mathematical Soc.}, address = {Providence, RI}, isbn = {978-1-4704-1551-8}, pages = {141 -- 152}, language = {en} } @phdthesis{Hilschenz, author = {Hilschenz, Michael}, title = {Ein Integralgleichungszugang zu den Minimalvektoren von Marx und Shiffman}, publisher = {Cuvillier}, address = {G{\"o}ttingen}, isbn = {978-3-95404-509-9}, pages = {147}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Surfaces of prescribed mean curvature H(x,y,z) with one-to-one central projection onto a plane}, series = {Pacific Journal of Mathematics}, volume = {281}, journal = {Pacific Journal of Mathematics}, number = {2}, issn = {0030-8730}, doi = {10.2140/pjm.2016.281.481}, pages = {481 -- 509}, language = {en} } @book{Kuennemann, author = {K{\"u}nnemann, Andreas}, title = {L{\"o}sbarkeit von Randwertproblemen mittels komplexer Integralgleichungen}, publisher = {Springer Spektrum}, address = {Wiesbaden}, isbn = {978-3-658-13126-5}, pages = {XII, 111}, language = {de} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Maximum Principle for H-Surfaces in the Unit Cone and Dirichlet's Problem for their Equation in Central Projection}, series = {Milan Journal of Mathematics}, volume = {84}, journal = {Milan Journal of Mathematics}, number = {1}, issn = {1424-9286}, doi = {10.1007/s00032-016-0250-9}, pages = {91 -- 104}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Multiple solutions for the nonparametric Plateau problem within the Euclidean space Rᴾ of arbitrary dimension}, series = {Calculus of Variations and Partial Differential Equations}, volume = {55}, journal = {Calculus of Variations and Partial Differential Equations}, number = {6, Artikel 140}, issn = {0944-2669}, doi = {10.1007/s00526-016-1087-3}, pages = {1 -- 28}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Solution of boundary value problems for surfaces of prescribed mean curvature H (x, y, z) with 1-1 central projection via the continuity method}, series = {Lithuanian mathematical journal}, volume = {58}, journal = {Lithuanian mathematical journal}, number = {3}, issn = {1573-8825}, doi = {10.1007/s10986-018-9399-y}, pages = {320 -- 328}, abstract = {When we consider surfaces of prescribed mean curvature H with a one-to-one orthogonal projection onto a plane, we have to study the nonparametric H-surface equation. Now the H-surfaces with a one-to-one central projection onto a plane lead to an interesting elliptic differential equation, which has been discovered for the case H = 0 already by T. Rad{\´o} in 1932. We establish the uniqueness of the Dirichlet problem for this H-surface equation in central projection and develop an estimate for the maximal deviation of large H-surfaces from their boundary values, resembling an inequality by J. Serrin from 1969. We solve the Dirichlet problem for nonvanishing H with compact support via a nonlinear continuity method. Here we introduce conformal parameters into the surface and study the well-known H-surface system. Then we combine these investigations with a differential equation for its unit normal, which has been developed by the author for variable H in 1982. Furthermore, we construct large H-surfaces bounding extreme contours by an approximation. Here we only provide an overview on the relevant proofs; for the more detailed derivations of our results, we refer the readers to the author's investigations in the Pacific Journal of Mathematics and the Milan Journal of Mathematics.}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Spektraltheorie selbstadjungierter Operatoren im Hilbertraum und elliptischer Differentialoperatoren}, publisher = {Springer Spektrum}, address = {Heidelberg [u.a]}, isbn = {978-3-662-58069-1}, doi = {10.1007/978-3-662-58069-1}, pages = {xi, 259}, language = {de} } @article{HauerHeLiu, author = {Hauer, Daniel and He, Yuhan and Liu, Dehui}, title = {Fractional Powers of Monotone Operators in Hilbert Spaces}, series = {Advanced Nonlinear Studies}, volume = {19}, journal = {Advanced Nonlinear Studies}, number = {4}, publisher = {Walter de Gruyter GmbH}, issn = {1536-1365}, doi = {10.1515/ans-2019-2053}, pages = {717 -- 755}, abstract = {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. Br{\´e}zis, {\´E}quations d'{\´e}volution du second ordre associ{\´e}es {\`a} des op{\´e}rateurs 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].}, language = {en} } @article{HauerMazon, author = {Hauer, Daniel and Maz{\´o}n, Jos{\´e} M.}, title = {Kurdyka-Łojasiewicz-Simon inequality for gradient flows in metric spaces}, series = {Transactions of the American Mathematical Society}, volume = {372}, journal = {Transactions of the American Mathematical Society}, number = {7}, publisher = {American Mathematical Society (AMS)}, issn = {0002-9947}, doi = {10.1090/tran/7801}, pages = {4917 -- 4976}, language = {en} } @article{ChillHauerKennedy, author = {Chill, Ralph and Hauer, Daniel and Kennedy, James}, title = {Nonlinear semigroups generated by j-elliptic functionals}, series = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es}, volume = {105}, journal = {Journal de Math{\´e}matiques Pures et Appliqu{\´e}es}, number = {3}, publisher = {Elsevier BV}, issn = {0021-7824}, doi = {10.1016/j.matpur.2015.11.005}, pages = {415 -- 450}, language = {en} } @article{GoldsteinHauerRhandi, author = {Goldstein, Jerome A. and Hauer, Daniel and Rhandi, Abdelaziz}, title = {Existence and nonexistence of positive solutions of p-Kolmogorov equations perturbed by a Hardy potential}, series = {Nonlinear Analysis}, volume = {131}, journal = {Nonlinear Analysis}, publisher = {Elsevier BV}, issn = {0362-546X}, doi = {10.1016/j.na.2015.07.016}, pages = {121 -- 154}, language = {en} } @article{Hauer, author = {Hauer, Daniel}, title = {The p-Dirichlet-to-Neumann operator with applications to elliptic and parabolic problems}, series = {Journal of Differential Equations}, volume = {259}, journal = {Journal of Differential Equations}, number = {8}, publisher = {Elsevier BV}, issn = {0022-0396}, doi = {10.1016/j.jde.2015.04.030}, pages = {3615 -- 3655}, language = {en} } @article{DancerDanersHauer, author = {Dancer, E.N. and Daners, Daniel and Hauer, Daniel}, title = {Uniform convergence of solutions to elliptic equations on domains with shrinking holes}, series = {Advances in Differential Equations}, volume = {20}, journal = {Advances in Differential Equations}, number = {5/6}, publisher = {Khayyam Publishing, Inc}, issn = {1079-9389}, doi = {10.57262/ade/1427744013}, pages = {463 -- 494}, language = {en} } @misc{Hauer, author = {Hauer, Daniel}, title = {Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval: the singular case}, series = {Nonlinear Differential Equations and Applications NoDEA}, volume = {20 (2013)}, journal = {Nonlinear Differential Equations and Applications NoDEA}, number = {3}, publisher = {Springer Science and Business Media LLC}, issn = {1021-9722}, doi = {10.1007/s00030-012-0203-0}, pages = {1171 -- 1190}, language = {en} } @misc{CollierHauer, author = {Collier, Timothy Allen and Hauer, Daniel}, title = {A density result for doubly nonlinear operators in L1}, series = {Discrete and Continuous Dynamical Systems - S}, volume = {17}, journal = {Discrete and Continuous Dynamical Systems - S}, number = {4}, publisher = {American Institute of Mathematical Sciences (AIMS)}, issn = {1937-1632}, doi = {10.3934/dcdss.2024031}, pages = {1663 -- 1671}, language = {en} } @misc{GurkaHauer, author = {Gurka, Petr and Hauer, Daniel}, title = {More insights into the Trudinger-Moser inequality with monomial weight}, series = {Calculus of Variations and Partial Differential Equations}, volume = {60}, journal = {Calculus of Variations and Partial Differential Equations}, publisher = {Springer Science and Business Media LLC}, issn = {0944-2669}, doi = {10.1007/s00526-020-01890-7}, pages = {27}, language = {en} } @misc{Hauer, author = {Hauer, Daniel}, title = {Regularizing effect of homogeneous evolution equations with perturbation}, series = {Nonlinear Analysis}, volume = {206}, journal = {Nonlinear Analysis}, publisher = {Elsevier BV}, issn = {0362-546X}, doi = {10.1016/j.na.2021.112245}, pages = {34}, language = {en} } @misc{AndrewsClutterbuckHauer, author = {Andrews, Ben and Clutterbuck, Julie and Hauer, Daniel}, title = {The fundamental gap for a one-dimensional Schr{\"o}dinger operator with Robin boundary conditions}, series = {Proceedings of the American Mathematical Society}, volume = {149}, journal = {Proceedings of the American Mathematical Society}, number = {4}, publisher = {American Mathematical Society (AMS)}, issn = {0002-9939}, doi = {10.1090/proc/15140}, pages = {1481 -- 1493}, language = {en} } @misc{AndrewsClutterbuckHauer, author = {Andrews, Ben and Clutterbuck, Julie and Hauer, Daniel}, title = {Non-concavity of the Robin ground state}, series = {Cambridge Journal of Mathematics}, volume = {8}, journal = {Cambridge Journal of Mathematics}, number = {2}, publisher = {International Press of Boston}, issn = {2168-0930}, doi = {10.4310/cjm.2020.v8.n2.a1}, pages = {243 -- 310}, language = {en} } @misc{ArendtHauer, author = {Arendt, Wolfgang and Hauer, Daniel}, title = {Maximal L2-regularity in nonlinear gradientsystems and perturbations of sublinear growth}, series = {Pure and Applied Analysis}, volume = {2}, journal = {Pure and Applied Analysis}, number = {1}, publisher = {Mathematical Sciences Publishers}, issn = {2578-5885}, doi = {10.2140/paa.2020.2.23}, pages = {23 -- 34}, language = {en} } @article{HauerMazon, author = {Hauer, Daniel and Maz{\´o}n, Jos{\´e} M.}, title = {Regularizing effects of homogeneous evolution equations: the case of homogeneity order zero}, series = {Journal of Evolution Equations}, volume = {19}, journal = {Journal of Evolution Equations}, number = {4}, publisher = {Springer Science and Business Media LLC}, issn = {1424-3199}, doi = {10.1007/s00028-019-00502-y}, pages = {965 -- 996}, language = {en} } @book{Sauvigny, author = {Sauvigny, Friedrich}, title = {Analysis}, edition = {2}, publisher = {Springer Berlin Heidelberg}, address = {Berlin, Heidelberg}, isbn = {978-3-662-69864-8}, doi = {10.1007/978-3-662-69865-5}, pages = {625}, language = {en} } @misc{Sauvigny, author = {Sauvigny, Friedrich}, title = {Minimal graphs in Riemannian spaces}, series = {Calculus of Variations and Partial Differential Equations}, volume = {63}, journal = {Calculus of Variations and Partial Differential Equations}, number = {5}, issn = {1432-0835}, doi = {10.1007/s00526-024-02704-w}, pages = {1 -- 47}, language = {en} }