2019
Том 71
№ 11

# Bonafede S.

Articles: 3
Article (English)

### On Hölder continuity of solutions of doubly nonlinear parabolic equations with weight

Ukr. Mat. Zh. - 1999. - 51, № 7. - pp. 890–903

We prove the Hölder regularity of bounded weak solutions of doubly nonlinear degenerate parabolic equations with measurable coefficients.

Article (Russian)

### Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. II

Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1601–1609

We use energy methods to prove the existence and uniqueness of solutions of the Dirichlet problem for an elliptic nonlinear second-order equation of divergence form with a superlinear tem [i.e., g(x, u)=v(x) a(x)⋎u⋎ p−1u,p>1] in unbounded domains. Degeneracy in the ellipticity condition is allowed. Coefficients a i,j(x,r) may be discontinuous with respect to the variable r.

Article (Ukrainian)

### Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I

Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 867-875

This paper is concerned with the existence and uniqueness of variational solutions of the strongly nonlinear equation $$- \sum\limits_1^m {_i \frac{\partial }{{\partial x_i }}\left( {\sum\limits_1^m {_j a_{i,j} (x, u(x))\frac{{\partial u(x)}}{{\partial x_j }}} } \right) + g(x, u(x)) = f(x)}$$ with the coefficients a i,j (x, s) satisfying an eHipticity degenerate condition and hypotheses weaker than the continuity with respect to the variable s. Furthermore, we establish a condition on f under which the solution is bounded in a bounded open subset Ω of Rm.