Ibraguimov A., Nazarov A.I. On Phragmen — Lindelof Principle for Non-Divergence Type Elliptic Equations and Mixed Boundary Conditions

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https://doi.org/10.15688/mpcm.jvolsu.2017.3.5

Akif Ibraguimov
Doctor of Physical and Mathematical Sciences, Professor,
Department of Mathematics and Statistics,
Texas Tech University
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Box 41042, Lubbock, TX 79409-1042, USA

Alexander I. Nazarov
Doctor of Physical and Mathematical Sciences, Professor,
Department of Mathematical Physics,
Saint Petersburg State University,
Prosp. Universitetsky, 28, 198504 Saint Petersburg, Peterhof, Russian Federation; ,
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Senior Researcher, St. Petersburg Department of Steklov Institute of Mathematics of
RAS,
Fontanka St. 27, 191023 St. Petersburg, Russian Federation

Abstract. The paper is dedicated to qualitative study of the solution of the Zaremba-type problem in Lipschitz domain with respect to the elliptic equation in non-divergent form. Main result is Landis type Growth Lemma in spherical layer for Mixed Boundary Value Problem in the class of “admissible domain”. Based on the Growth Lemma Phragmén — Lindelöf theorem is proved at junction point of
Dirichlet boundary and boundary over which derivative in non-tangential direction is defined.

Key words: elliptic equation in non-divergent form, Mixed Boundary Value Problem, Growth Lemma, Phragmén — Lindelöf theorem, Zaremba-type problem.

On Phragmen — Lindelof Principle for Non-Divergence Type Elliptic Equations and Mixed Boundary Conditions by Ibraguimov A., Nazarov A.I. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. №3 (40) 2017 pp. 65-76

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