On the fractional p-Laplacian problem via Young measures

Document Type : Original Article

Authors

Ihya TALIBI

Farah Balaadich

Brahim El Boukari

Jalila El Ghordaf

Laboratory of Applied Mathematics and Scientific Computing‎, ‎Sultan Moulay Slimane University‎, ‎Beni‎ ‎ Mellal‎, ‎Morocco

10.22034/kjm.2024.475795.3304

Abstract

In this paper we study the existence results for a parabolic problem of the following form:
$$\begin{cases}
\frac{\partial u}{\partial t}+ (-\Delta)_p^s u=f & \text { in } \Omega\times(0,T), \\ u=0 & \text { in } (\mathbb{R}^n\backslash\Omega)\times(0,T), \\ u(x, 0)=u_0(x) & \text { in } \Omega,
\end{cases}$$
where $\Omega\subset\mathbb{R}^n$ and $(-\Delta)_p^s$ is the fractional $p$-Laplacian. Under appropriate assumptions concerning the main functions, the existence of weak solutions is obtained by applying the Galerkin method combined with the theory of Young measures.

Keywords

35A01

35K60

35K55

Subjects

• 35 Partial differential equations

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