The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids. We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.
On certain surface integrals related to the conormal derivative problem / Palagachev, Dian K.. - In: PARTIAL DIFFERENTIAL EQUATIONS IN APPLIED MATHEMATICS. - ISSN 2666-8181. - STAMPA. - 17:(2026). [10.1016/j.padiff.2025.101325]
On certain surface integrals related to the conormal derivative problem
Dian K. Palagachev
2026
Abstract
The non-homogeneous conormal derivative problems for nonlinear, second-order divergence form elliptic equations with singular data appear naturally in mathematical modeling of real phenomena involving problems of image recovery, the thermistor problem, or studies of non-Newtonian fluids. We prove suitable estimates for certain surface integrals, related to non-homogeneous conormal derivative problems, which lead to essential boundedness of the weak solutions under quite general hypotheses on the data.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
