Linear Parabolic Mixed Problems in Spaces of Hölder Continuous Functions: Old and New Results

Davide Guidetti


We illustrate some old and new results, concerning linear parabolic mixed problems in spaces of Hölder continuous functions: we begin with the classical Dirichlet and oblique derivative problems and continue with dynamic and Wentzell boundary conditions.

Full Text:

PDF (English)


H. Amann, J. Escher, "Strongly Continuous Dual Semigroups", Ann. Mat. Pura Appl., vol. CLXXI (1996), 41-62.

J. Escher, "Quasilinear parabolic systems with dynamical boundary conditions", Commun. Part. Diff. Eq. 18 (1993), 1309-1364.

A. Favini, G. Ruiz Goldstein, J. Goldstein, E. Obrecht, S. Romanelli, "Elliptic operators with general Wentzell boundary conditions, analytic semigroups and the angle concavity theorem", Math. Nachr. 283 (2010), 504-521.

A. Favini, G. Ruiz Goldstein, J. Goldstein, S. Romanelli, "The heat equation with generalized Wentzell boundary conditions", J. evol. equ. 2 (2002), 1-19.

D. Guidetti, "Abstract elliptic problems depending on a parameter and parabolic problems with dynamic boundary conditions", Springer Indam Series 10 (2014).

D. Guidetti, "Linear parabolic problems with dynamic boundary conditions in spaces of Hölder continuous functions", Ann. Mat. Pura Appl. 195 (2016), 167-198.

D. Guidetti, "Parabolic problems with general Wentzell boundary conditions and diffusion on the boundary", Commun. Pure Appl. Analysis 15 (2016), 1401-1417.

D. Hömberg, K. Krumbiegel, J. Rehberg, "Optimal control of a parabolic equation with dynamic boundary conditions", Appl. Math. Optim. 67 (2013), 3-31.

O. A. Ladyzhenskaja, V.A. Solonnikov, N.N. Ural'ceva, Linear and quasilinear equations of parabolic type, Transl. Math. Monographs, AMS, Providence (1968).

R. E. Langer, "A problem in diffusion or in the ow of heat for a solid in contact with a fluid", Tohoku Math. Journ. 35 (1932), 260-275.

A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser (1995).

D. Mugnolo, S. Romanelli, "Dynamic and generalized Wentzell node conditions for network equations", Math. Meth. Appl. Sci. 30 (2007), 681-706.

G. Ruiz Goldstein, "Derivation and physical interpretation of general boundary conditions", Adv. Diff. Eq. 11 (2006), 457-480.

J. L. Vazquez, E. Vitillaro, "Heat equation with dynamical boundary conditions of reactive-diffusive type", J. Diff. Eq. 250 (2011), 2143-2161.

DOI: 10.6092/issn.2240-2829/6697


  • There are currently no refbacks.

Copyright (c) 2016 Davide Guidetti Guidetti

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 Unported License.

Creative Commons License 

ISSN 2240-2829
Registration at Bologna Law Court no. 8138 on 24th November, 2010

The journal is hosted and mantained by ABIS-AlmaDL [privacy]