$W^{1,1}_0(\Omega)$ in some borderline cases of elliptic equations with degenerate coercivity
Lucio Boccardo, Gisella Croce (LMAH)
TL;DR
This paper investigates a specific class of degenerate elliptic equations, establishing the existence of distributional solutions in challenging borderline cases where standard coercivity conditions fail.
Contribution
It provides new existence results for solutions in borderline degenerate coercivity scenarios, expanding understanding of elliptic equations with degenerate behavior.
Findings
Existence of distributional solutions in borderline cases
Extension of elliptic theory to degenerate coercivity scenarios
Identification of conditions ensuring solutions exist
Abstract
We study a degenerate elliptic equation, proving existence results of distributional solutions in some borderline cases.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Partial Differential Equations · Stability and Controllability of Differential Equations