Quasilinear elliptic systems with a drift term: Existence and regularity

Key Points

• The main aim is to investigate the existence and regularity of weak solutions in quasilinear elliptic systems with a drift term.
• Studied a quasilinear system with drift in bounded domain Ω ⊂ R n for n ≥ 3.
• Assumed support for off-diagonal coefficients lies within a geometrically increasing staircase structure.
• Proved L p -regularity for weak solutions across any p in [1, +∞) with small L n -norm condition.
• Established existence of at least one weak solution under the condition that the L n -norm of the drift term is sufficiently small.
• Proved that weak solutions achieve L p -regularity for any chosen p within the range.
• Demonstrated the significance of geometric arrangement of coefficients on solution properties.