scholarly journals A Hopf-type Boundary Point Lemma for Pairs of Solutions to Quasilinear Equations

2019 ◽  
Vol 62 (3) ◽  
pp. 607-621 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Weak Solutions ◽  
Boundary Point ◽  
Quasilinear Equation ◽  
Divergence Form ◽  
Quasilinear Equations ◽  
Differentiable Functions ◽  
The Difference ◽  
Type Boundary

AbstractWe present a Hopf boundary point lemma for the difference between two Hölder continuously differentiable functions, each weak solutions to a divergence-form quasilinear equation, under mild boundedness assumptions on the coefficients of this equation.

scholarly journals Existence and multiplicity results for quasilinear equations in the Heisenberg group

2019 ◽  
Vol 39 (2) ◽  
pp. 247-257 ◽  
Author(s):  
Patrizia Pucci
Keyword(s):  
Heisenberg Group ◽  
Quasilinear Equation ◽  
Divergence Form ◽  
Infinitely Many Solutions ◽  
Entire Solutions ◽  
Quasilinear Equations ◽  
Multiplicity Results ◽  
Minimax Theory ◽  
Existence And Multiplicity ◽  
General Elliptic

In this paper we complete the study started in [Existence of entire solutions for quasilinear equations in the Heisenberg group, Minimax Theory Appl. 4 (2019)] on entire solutions for a quasilinear equation \((\mathcal{E}_{\lambda})\) in \(\mathbb{H}^{n}\), depending on a real parameter \(\lambda\), which involves a general elliptic operator \(\mathbf{A}\) in divergence form and two main nonlinearities. Here, in the so called sublinear case, we prove existence for all \(\lambda\gt 0\) and, for special elliptic operators \(\mathbf{A}\), existence of infinitely many solutions \((u_k)_k\).

scholarly journals Generalizing Hopf’s Boundary Point Lemma

2019 ◽  
Vol 62 (1) ◽  
pp. 183-197 ◽  
Author(s):  
Leobardo Rosales
Keyword(s):  
Weak Solutions ◽  
Lower Order ◽  
Boundary Point ◽  
Elliptic Equations ◽  
Morrey Space ◽  
Divergence Form ◽  
Hölder Continuous

AbstractWe give a Hopf boundary point lemma for weak solutions of linear divergence form uniformly elliptic equations, with Hölder continuous top-order coefficients and lower-order coefficients in a Morrey space.

scholarly journals $L^{\infty }$ decay estimates of solutions of nonlinear parabolic equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hui Wang ◽  
Caisheng Chen
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Nonlinear Parabolic Equation ◽  
Divergence Form ◽  
Decay Estimates ◽  
Laplacian Equation ◽  
Estimates Of Solutions ◽  
Nonlinear Parabolic ◽  
Doubly Nonlinear ◽  
Doubly Nonlinear Parabolic Equation

AbstractIn this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and the degenerate evolution m-Laplacian equation not in the divergence form. By a modified Moser’s technique we obtain $L^{\infty }$ L ∞ decay estimates of weak solutiona.

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

Radiative effects for some bidimensional thermoelectric problems

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Luisa Consiglieri
Keyword(s):  
Steady State ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Sufficient Conditions ◽  
Coupled System ◽  
Divergence Form ◽  
Radiative Effects ◽  
Existence Of Weak Solutions ◽  
Nonlinear Radiation ◽  
Radiation Type

AbstractThere are two main objectives in this paper. One is to find sufficient conditions to ensure the existence of weak solutions for some bidimensional thermoelectric problems. At the steady-state, these problems consist of a coupled system of elliptic equations of the divergence form, commonly accomplished with nonlinear radiation-type conditions on at least a nonempty part of the boundary of a

Existence of solution for quasilinear equations involving local conditions

2019 ◽  
Vol 150 (6) ◽  
pp. 3074-3086
Author(s):  
Patricio Cerda ◽  
Leonelo Iturriaga
Keyword(s):  
Continuous Function ◽  
Nonlinear Term ◽  
Quasilinear Equation ◽  
Existence Of Solution ◽  
Positive Parameter ◽  
Quasilinear Equations ◽  
Local Conditions ◽  
Existence Of Weak Solutions ◽  
Carathéodory Function ◽  
Image Position

AbstractIn this paper, we study the existence of weak solutions of the quasilinear equation \begin{cases} -{\rm div} (a(\vert \nabla u \vert ^2)\nabla u)=\lambda f(x,u) &{\rm in} \ \Omega,\\ u=0 &{\rm on} \ \partial\Omega, \end{cases}where a : ℝ → [0, ∞) is C1 and a nonincreasing continuous function near the origin, the nonlinear term f : Ω × ℝ → ℝ is a Carathéodory function verifying certain superlinear conditions only at zero, and λ is a positive parameter. The existence of the solution relies on C1-estimates and variational arguments.

scholarly journals On the rate of the volume growth for symmetric viscous heat-conducting gas flows with a free boundary

2006 ◽  
Vol 2006 ◽  
pp. 1-8
Author(s):  
Alexander Zlotnik
Keyword(s):  
Free Boundary ◽  
Weak Solutions ◽  
Volume Growth ◽  
External Boundary ◽  
Gas Flows ◽  
Positive Density ◽  
Heat Conducting ◽  
Quasilinear Equations ◽  
Viscous Heat ◽  
Gas Volume

The system of quasilinear equations for symmetric flows of a viscous heat-conducting gas with a free external boundary is considered. For global in time weak solutions having nonstrictly positive density, the linear in time two-sided bounds for the gas volume growth are established.

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