Rios Soto, KarenMesino Espinosa, Efren2024-07-152024-07-152024-07-10https://hdl.handle.net/20.500.11801/3729Let Ω ⊆ R^N be a bounded (ε, δ)-domain with boundary a d-set, for N ≥ 2. We investigate the solvability and establish a priori estimates for the generalized elliptic quasi-linear fractional problem involving the regional fractional p-Laplace operator with Neumann or Robin boundary conditions. First, we prove the existence and uniqueness of weak solutions for the problem, and we show that such solutions are globally bounded. Moreover, we establish a priori estimates for the difference of weak solutions of our problem. Additionally, we present results on inverse positivity and a weak comparison principle.Sea Ω ⊂ RN un dominio-(ε, δ) acotado con frontera un d-conjunto, para N ≥ 2. Investigamos la solvabilidad y establecemos estimaciones a priori para el problema eliptico cuasi-lineal generalizado fraccional que involucra el p-operador de Laplace fraccional regional con condiciones de frontera de Neumann o Robin. Primero, demostramos la existencia y unicidad de soluciones debiles para el problema, y mostramos que dichas soluciones est ́an acotadas globalmente. Adem ́as, establecemos estimaciones a priori para la diferencia de soluciones debiles de nuestro problema. Adicionalmente, presentamos resultados sobre positividad inversa y un principio de comparacion debil.enAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-sa/4.0/Generalized elliptic quasi-linear fractional problemFractional p-Laplace operatorA priori estimatesWeak comparison principleInverse positivityHarmonic functionsFractional differential equationsBoundary element methodsThesis(c) 2024 Efren Mesino Espinosa