| Abstract: |
| We present a boundedness result for weak solutions to a class of two-weight degenerate elliptic equations. The motivating example is the equation governing the static equilibrium of a spider orb web, whose continuous membrane model was proposed by Morassi, Soler and Zaera in 2017. The concentration of radial threads near the center induces a singularity at the origin. This is reflected in the degenerate character of the equation of the model through two weights whose ratios are neither bounded away from zero nor bounded from above. Our approach combines a refined two-weight Sobolev-Poincar\`e inequality with the assumption that lower-order coefficients belong to a generalized Stummel-Kato class. These tools, together with a generalized Moser iteration scheme, yield an explicit $L^\infty$ bound for weak solutions in terms of the data and the weights. |
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