Page 696 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 696
POSTER SESSION
Maximal regularity for evolution equations and application to the Stefan
problem
Martin Lukarevski, martinton@yahoo.com
University "Goce Delcev" - Stip, North Macedonia
Maximal regularity is a useful tool for solving abstract parabolic evolution equations. A variant
of the one-phase quasistationary Stefan problem that we consider can be reduced to a single
evolution equation. We tackle this problem using H∞-calculus to show that the operator in
the evolution equation has maximal regularity and then apply an existence theorem for this
type of evolution equation. We use additionally an assumption that one particular result on the
solvability of a degenerate oblique derivative problem extends in an appropriate way.
Generalizations of Steffensen’s inequality by interpolating polynomials
Anamarija Perušic´ Pribanic´, anamarija.perusic@uniri.hr
Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia
Coauthors: Josip Pecˇaric´, Ana Vukelic´
In papers [1, 2, 3] we obtain new generalizations of Steffensen’s inequality using two-point
Abel-Gontscharoff polynomial, Hermite interpolating polynomials and Lidstone’s polynomial.
Here we present results obtained by one of the polynomials i.e. Lidstone’s polynomial. Firstly,
we give few valuable identities and then using these identities we prove new generalizations
of Steffensen’s inequality for (2n)−convex and (2n + 1)−convex functions. Further, using
Cˇ ebyšev and Grüss type inequalities we consider the bounds for the integrals in the perturben
versions of the previously described identities.
References
[1] J. Pecˇaric´, A. Perušic´ Pribanic´, K. Smoljak Kalamir, Generalizations of Steffensen’s in-
equality via two-point Abel-Gontscharoff polynomial, Analele Stiintifice ale Universitatii
Ovidius Constanta-Seria Matematica, 27 (2019), 2; 121-137.
[2] J. Pecˇaric´, A. Perušic´ Pribanic´, K. Smoljak Kalamir, Integral error representation of
Hermite interpolating polynomials and related generalizations of Steffensen’s inequality,
MIA, 22 (2019), 4; 1177-1191.
[3] J. Pecˇaric´, A. Perušic´ Pribanic´, A. Vukelic´, Generalizations of Steffensen’s inequality by
Lidstone’s polynomial and related results , Quaestiones Mathematicae 43 (2020), 3; 293-
307.
694
Maximal regularity for evolution equations and application to the Stefan
problem
Martin Lukarevski, martinton@yahoo.com
University "Goce Delcev" - Stip, North Macedonia
Maximal regularity is a useful tool for solving abstract parabolic evolution equations. A variant
of the one-phase quasistationary Stefan problem that we consider can be reduced to a single
evolution equation. We tackle this problem using H∞-calculus to show that the operator in
the evolution equation has maximal regularity and then apply an existence theorem for this
type of evolution equation. We use additionally an assumption that one particular result on the
solvability of a degenerate oblique derivative problem extends in an appropriate way.
Generalizations of Steffensen’s inequality by interpolating polynomials
Anamarija Perušic´ Pribanic´, anamarija.perusic@uniri.hr
Faculty of Civil Engineering, University of Rijeka, Rijeka, Croatia
Coauthors: Josip Pecˇaric´, Ana Vukelic´
In papers [1, 2, 3] we obtain new generalizations of Steffensen’s inequality using two-point
Abel-Gontscharoff polynomial, Hermite interpolating polynomials and Lidstone’s polynomial.
Here we present results obtained by one of the polynomials i.e. Lidstone’s polynomial. Firstly,
we give few valuable identities and then using these identities we prove new generalizations
of Steffensen’s inequality for (2n)−convex and (2n + 1)−convex functions. Further, using
Cˇ ebyšev and Grüss type inequalities we consider the bounds for the integrals in the perturben
versions of the previously described identities.
References
[1] J. Pecˇaric´, A. Perušic´ Pribanic´, K. Smoljak Kalamir, Generalizations of Steffensen’s in-
equality via two-point Abel-Gontscharoff polynomial, Analele Stiintifice ale Universitatii
Ovidius Constanta-Seria Matematica, 27 (2019), 2; 121-137.
[2] J. Pecˇaric´, A. Perušic´ Pribanic´, K. Smoljak Kalamir, Integral error representation of
Hermite interpolating polynomials and related generalizations of Steffensen’s inequality,
MIA, 22 (2019), 4; 1177-1191.
[3] J. Pecˇaric´, A. Perušic´ Pribanic´, A. Vukelic´, Generalizations of Steffensen’s inequality by
Lidstone’s polynomial and related results , Quaestiones Mathematicae 43 (2020), 3; 293-
307.
694
