A regularity result for a class of non-uniformly elliptic operators
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DOI: 10.1007/s00013-022-01715-3
Abstract: We obtain an explicit Hölder regularity result for viscosity solutions of a class of second order fully nonlinear equations led by operators that are neither convex/concave nor uniformly elliptic. read more here.
Keywords: regularity result; uniformly elliptic; class non; result class ... See more keywords
Existence of Multiple Solutions for a Class Non-uniformly Elliptic Equations with Critical Exponential Growth
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DOI: 10.1007/s41980-018-0033-x
Abstract: This paper deals with the existence and multiplicity of weak solutions to non-uniformly elliptic problem $$\begin{aligned} -\text {div}(a(x,\nabla u))+V(x)\vert u\vert ^{N-2} u=\lambda \Bigg (\exp \Bigg (\alpha \vert u\vert ^{\frac{N}{N-1}}\Bigg )+f(x,u)\Bigg ), \end{aligned}$$-div(a(x,∇u))+V(x)|u|N-2u=λ(exp(α|u|NN-1)+f(x,u)),in $$\mathbb {R}^N$$RN, where… read more here.
Keywords: solutions class; vert; uniformly elliptic; multiple solutions ... See more keywords
Regularity of quasi-minimizers for non-uniformly elliptic integrals
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DOI: 10.1016/j.jmaa.2019.123838
Abstract: Abstract In this paper we consider a class of non-uniformly elliptic integral functionals and we prove the local boundedness of the quasi-minimizers. Our approach is based on a suitable adaptation of the celebrated De Giorgi… read more here.
Keywords: minimizers non; elliptic integrals; regularity quasi; uniformly elliptic ... See more keywords
Monotonicity of solutions for the uniformly elliptic nonlocal Bellman equation on the upper half space
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DOI: 10.1016/j.jmaa.2020.124843
Abstract: Abstract In this paper, we develop a sliding method for the uniformly elliptic nonlocal Bellman operator. We first establish a maximum principle on an upper half space, which plays an important role in the sliding… read more here.
Keywords: nonlocal bellman; half space; uniformly elliptic; upper half ... See more keywords
Construction of a unique mild solution of one-dimensional Keller-Segel systems with uniformly elliptic operators having variable coefficients
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DOI: 10.1515/ms-2017-0150
Abstract: Abstract A one-dimensional Keller-Segel system which is defined through uniformly elliptic operators having variable coefficients is considered. In the main theorems, the local existence and uniqueness of the mild solution of the system are proved.… read more here.
Keywords: one dimensional; uniformly elliptic; mild solution; solution ... See more keywords