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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").
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