Entropy solutions for strong nonlinear elliptic problem in Musielak-Orlicz-Sobolev spaces

Other Title(s)

الحلول الكونية لمشكلة القطع الناقص الغير خطية القوية في فضاءات ميزلاك-أورلكس-سبوليف

Joint Authors

al-Humi, Muhammad Ali Muhsin
al-Hamzah, Bassam Abd al-Qadir Atiq

Source

المجلة العلمية لجامعة إقليم سبأ : مجلة علمية نصفية محكمة

Publisher

University of Saba Region University Vice Rectorates for Postgraduate Studies and Scientific Research

Publication Date

2022-05-31

Country of Publication

Yemen

No. of Pages

18

Main Subjects

Mathematics

English Abstract

In this paper, we shall be concerned with the existence result of the following problem, $$\begin{aligned} \left\{ \begin{array}{l} -\text {div}\left( a(x,u,\nabla u)\right) -\text {div}(\Phi (x,u))= f \ \ \mathrm{in}\ \Omega ,\\ u=0 \text { on } \partial \Omega , \end{array} \right.

\end{aligned}$$ (0.1)with the second term f belongs to \(L^1(\Omega )\).

The growth and the coercivity conditions on the monotone vector field a are prescribed by a generalized N-function M.

We assume any restriction on M, therefore we work with Musielak–Orlicz spaces which are not necessarily reflexive.

The lower order term \(\Phi \) is a Carathéodory function satisfying only a growth condition.

Data Type

Conference Papers

Record ID

BIM-1421815

• APA
• MLA
• AMA