Quasilinear Riccati-Type Equations with Oscillatory and Singular Data

Autor: Nguyen Quoc-Hung, Phuc Nguyen Cong

Publikováno v: Advanced Nonlinear Studies, Vol 20, Iss 2, Pp 373-384 (2020)

We characterize the existence of solutions to the quasilinear Riccati-type equation

Externí odkaz: https://doaj.org/article/a5529bae9d17456f81232dc2dd7b914b

Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data

Autor: Laurent Veron, Marie-Françoise Bidaut-Véron, Quoc-Hung Nguyen

Publikováno v: Calculus of Variations and Partial Differential Equations
Calculus of Variations and Partial Differential Equations, Springer Verlag, 2020, 59:148, pp.1-38

We study the equation $$-\text {div}(A(x,\nabla u))=|u|^{q_1-1}u|\nabla u|^{q_2}+\mu $$ where $$A(x,\nabla u)\sim |\nabla u|^{p-2}\nabla u$$ in some suitable sense, $$\mu $$ is a measure and $$q_1$$ , $$q_2$$ are nonnegative real numbers and satisfy

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::39665082b5fac71742fa8e7672602932
https://hal.archives-ouvertes.fr/hal-01775096/file/Veron-NGUYEN.pdf

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The Hardy-Littlewood maximal function, Choquet integrals, and embeddings of Sobolev type.

Autor: Ooi, Keng Hao, Phuc, Nguyen Cong

Publikováno v: Mathematische Annalen; Apr2022, Vol. 382 Issue 3/4, p1865-1879, 15p

On a capacitary strong type inequality and related capacitary estimates

Autor: Ooi, Keng Hao, Phuc, Nguyen Cong

We establish a Maz'ya type capacitary inequality which resolves a special case of a conjecture by David R. Adams. As a consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This enables us to

Externí odkaz: http://arxiv.org/abs/2009.09291