What question did this study set out to answer?

The main aim is to investigate the existence and regularity of weak solutions in quasilinear elliptic systems with a drift term.

May 9, 2026Nonlinear AnalysisOpen Access

Quasilinear elliptic systems with a drift term: Existence and regularity

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Randomized trial investigates the existence of weak solutions in bounded domains, suggesting L p -regularity.

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.

Gironimo et al. (2026) studied this question.

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