Tomasz Adamowicz's Page
Associate Professor in the Department of Differential Equations
dr hab., prof. IMPAN
Institute of Mathematics Polish Academy of Sciences in Warsaw (IM PAN)
Phone: 22 522 81 80, 510
Email:
T(dot)Adamowicz(at)impan(dot)pl
Research Interests
Geometric Function and Mapping Theory
Geometric properties of elliptic PDEs and systems of PDEs
Analysis on metric measure spaces
p-Harmonic and Quasiregular Worlds
Variable exponent analysis and Nonstandard growth PDEs
Calculus of Variations
Simons Semester in Geometry and analysis in function and mapping theory on Euclidean and metric measure spaces at IM PAN,
September-November 2019
Seminar in Geometric Function and Mapping Theory at IM PAN
Geometric analysis and related topics /in honour of Tadeusz Iwaniec's 70th birthday
Geometric Function Theory meets Geometric Group Theory in Warsaw, Banach Center, IM PAN, 14-17 Oct 2015
Research meeting in Variable exponent theory and applications, Banach Center, IM PAN, 26-29 Oct 2014
Banach Center Publications, Volume 101: Calculus of Variations and PDEs
Lectures by Tadeusz Iwaniec, University of Warsaw, 15 Oct - 10 Dec 2014 (link to the webpage of P. Strzelecki)
Grants:
Grant Sonata 5 by NCN (Narodowe Centrum Nauki/National Science Center), 2014-2017, UMO 2013/09/D/ST1/03681
Grant Iuventus Plus by Ministry of Science and Higher Education, 2015-2017, Nr 0009/IP3/2015/73
Grant OPUS 13 by NCN (Narodowe Centrum Nauki/National Science Center), 2018-2021, UMO-2017/25/B/ST1/01955
PhD Students:
Antoni Kijowski, IM PAN, 4th year, planned graduation - Fall 2020
Tomasz Kostrzewa, MiNI PW (coadvisor: P. Górka), dissertation defended in January 2019
Publications and submitted manuscripts:
The Grötzsch problem in higher dimensions
Rend. Lincei Mat. Appl.
(18)
(2007), 163-177
On a variant of the maximum principle involving radial p-Laplacian with applications to nonlinear eigenvalue problems and nonexistence results (with A. Kałamajska)
Topol. Methods Nonlinear Anal.,
Volume 34, no. 1,
(2009), 1-20
On p-harmonic mappings in the plane
Nonlinear Anal.,
Volume 71, Issues 1-2,
1 July 2009-15 July 2009, 502-511
Mappings of finite distortion and PDE with nonstandard growth (with P. Hästö)
Int. Math. Res. Not. IMRN, (2010), 1940-1965,doi:10.1093/imrn/rnp192
Maximum principles and nonexistence results for radial solutions to equations involving p-Laplacian (with A. Kałamajska)
Math. Methods Appl. Sci.,
Volume 33, Issue 13,
(2010), 1618-1627
Non-conformal Loewner type estimates for modulus of curve families (with N. Shanmugalingam)
Ann. Acad. Sci. Fenn. Math.,
(35),
(2010), 609-626
Harnack's Inequality and The Strong p(x)-Laplacian (with P. Hästö)
J. Differential Equations,
Volume 250, Issue 3,
1 February 2011, 1631-1649
Remarks on time map for quasilinear equations (with P. Korman)
J. Math. Anal. Appl.
Volume 376, Issue 2,
15 April 2011, 686-695
Prime ends for domains in metric spaces (with A. Björn, J. Björn, N. Shanmugalingam)
Adv. Math.
238 (2013)
, 459-505
The geometry of planar p-harmonic mappings: convexity, level curves and the isoperimetric inequality
Ann. Sc. Norm. Super. Pisa.
Volume XIV(1),
2015, 263-292, doi: 10.2422/2036-2145.201201_010
Maximal operator in variable exponent Lebesgue spaces on unbounded quasimetric measure spaces (with P. Harjulehto and P. Hästö)
Math. Scand.
116 (1)
, 2015, 5-22
Regularity of p(.)-superharmonic functions, the Kellogg property and semiregular boundary points (with A. Björn, J. Björn)
Ann. Inst. H. Poincaré Anal. Non Linéaire,
31 (6)
, 2014, 1131-1153, doi: 10.1016/j.anihpc.2013.07.012
Phragmen-Lindelöf theorems for equations with nonstandard growth
Nonlinear Anal.
Vol. 97,
March 2014, 169-184
The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(.)-harmonic measures (with N. Lundström)
Ann. Mat. Pura Appl. ,
195(2)
2016, 623-658 doi: 10.1007/s10231-015-0481-3
Three-spheres theorem for p-harmonic mappings
Calc. Var. PDEs,
53(3)
2015, 1015-1032, doi: 10.1007/s00526-014-0775-0
The Liouville theorems for elliptic equations with nonstandard growth (with P. Górka)
Commun. Pure Appl. Anal.
14(6)
2015, 2377-2392.
Three-spheres theorems for subelliptic quasilinear equations in Carnot groups of Heisenberg-type (with B. Warhurst)
Proceedings of AMS
144(10)
2016, 4291-4302.
Hölder continuity of quasiminimizers with nonstandard growth (with O. Toivanen)
Nonlinear Anal.
Vol. 125,
September 2015, 433-456
Prime ends in the Heisenberg group H1 and the boundary behavior of quasiconformal mappings (with B. Warhurst)
Ann. Acad. Sci. Fenn. Math.,
43(2)
2018, 1-38
Harmonic functions on metric measure spaces (with M. Gaczkowski and P. Górka)
Rev. Math. Complut.,
32(1)
2019, 141-186, doi.org/10.1007/s13163-018-0272-7
Prime ends in metric spaces and boundary extensions of mappings
Anal. Math. Phys.,
9
2019, 1941-1975, doi.org/10.1007/s13324-019-00292-z
Mean value property and harmonicity on Carnot-Caratheodory groups (with B. Warhurst)
Potential Anal.,
52
2020, 497-525, doi.org/10.1007/s11118-018-9740-4
A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group (with K. Faessler and B. Warhurst)
Ann. Mat. Pura Appl.,
199
2020, 147-186, doi.org/10.1007/s10231-019-00871-8
The Rado-Kneser-Choquet theorem for p-harmonic mappings between Riemannian surfaces (with J. Jääskeläinen, A. Koski)
Rev. Math. Iberoam.,
36(6)
2020 doi.org/10.4171/rmi/1183
The prime end capacity of inaccessible prime ends, resolutivity, and the Kellogg property (with N. Shanmugalingam)
Math. Zeit.,
Vol. 293, Issue 3-4
2019, 1633-1656 doi.org/10.1007/s00209-019-02268-y
Variational approach to the asymptotic mean-value property for the p-Laplacian on Carnot groups (with A. Kijowski, A. Pinamonti and B. Warhurst)
Nonlinear Analysis,
Vol. 198,
September 2020, doi.org/10.1016/j.na.2020.111893
Asymptotically mean value harmonic functions in doubling metric measure spaces (with A. Kijowski and E. Soultanis)
submitted
Hardy spaces for quasiregular mappings and composition operators (with M.J. Gonzalez)
accepted to Journal of Geometric Analysis
Isoperimetric inequalities and geometry of level curves of harmonic functions on smooth and singular surfaces (with G. Veronelli)
submitted
Teaching
Some of my teaching evaluations are available here
(1 - min, 5 - max):
Spring 2003, Fall 2003: Linear Algebra with Geometry. (Recitations)
Fall 2005, Fall 2006: Calculus 1. (Recitations)
Spring 2007, Fall 2007, Spring 2008: Calculus 3.
Fall 2008:
Calculus 2.
Winter 2009:
Calculus 3.
Spring 2009:
Calculus 4 (Section 1),
Calculus 4 (Section 2).
Fall 2009:
Differential Equations (Section 1),
Differential Equations (Section 2).
Winter 2010:
Calculus 1.
Spring 2010:
Calculus 2.
Fall(1st half) 2011, 2012: Flervariabelanalys (Calculus 3-4)
Fall(2nd half) 2010, 2011: Envariabelanalys 1 (Calculus 1)
Fall 2011, 2012: Linear Algebra
Winter 2011, 2012, 2013: Envariabelanalys 2 (Calculus 2-3)
Spring 2011, 2012, 2013: Flervariabelanalys (Calculus 3-4)
Some links
Institute of Mathematics Polish Academy of Sciences in Warsaw
Calculus of Variations and PDEs, Szczawnica 9-12 July 2012, a satellite conference of 6th ECM
Department of Mathematics, Linköping University
Graduate Student Seminar at University of Cincinnati
Department of Mathematical Sciences, University of Cincinnati
Mathematics Graduate Organization (MGO) at Syracuse University
Department of Mathematics, Syracuse University
Faculty of Mathematics, Informatics and Mechanics, University of Warsaw
Banach Center, Poland