An Analysis of Quasilinear Elliptic Systems with L^{\infty}-Type Data


Abstract


The present study establishes the existence and uniqueness of a solution of weak energy for a boundary value problem within a smooth, bounded, open domain \Omega in \mathbb{R}^{n} where n \geq 3 . The problem is defined by the following equation: \begin{cases} {-div} \left[a(z,\upsilon,D\upsilon)\right]+\vert \upsilon\vert^{p{(z)}-2}\upsilon =f & \text { in } \Omega, \\ ~~ \upsilon =0 & \text { on } \partial \Omega, \end{cases} where the function f is constrained to lie within the space L^{\infty}\left(\Omega ; \mathbb{R}^{m}\right). The proof of existence relies on the utilization of the concept of Young measures.

DOI Code: 10.1285/i15900932v44n2p113

Keywords: Quasilinear elliptic systems; weak energy solution; Young measure; p(z)-variable exponents

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