Regularity for solutions of partial differential equations with irregular coefficients

The research program analyzes how the regularity of coefficients affects the integrability and higher differentiability of solutions to nonlinear elliptic equations in divergence form, identifying quantitative estimates for higher-order gradient regularity even with discontinuous spatial dependence (Sobolev or Besov spaces). Starting from standard growth equations and local gradient estimates, the study will address non-standard growth problems and parabolic equations, identifying minimal regularity assumptions on the coefficients and providing examples and counterexamples. Scientific supervisor: Prof. Antonia Passarelli di Napoli (Project "000022_BUDGET_ECONOMICO_RICERCA_2026").